If William truly was born in 1818, then he is not Tollison's son because Tollison & Jane were married in 1820 and have no children with them in the 1820 census (q.v.), but it does appear that what's wrong here is the 1818 birthyear and that Tollison & Jane are, indeed, his parents.  William is younger than his wife, Mary, so she may be the one who inflated his age.

— born in GA, either in Elbert Co. or Franklin Co., GA:
4.  Elizabeth J. TYNER, b. Jun 1852
5.  John Chapel "Chap" TYNER, b. 25 Aug 1853; d. 20 Jul 1923, Madison Co., GA
6.  Cornelia Mary TYNER, b. 13 Jun 1855; d. 5 Sep 1884
7.  Benson William / William Benson TYNER, b. 1856; d. 20 Nov 1921, Griffin, Spalding Co., GA
8.  Sarah F. TYNER, b. 1860; d. by 1870

1.  Jordan R. Dodd, ed.  1993.  Georgia Marriages: Early to 1850.  Liahona Research, Orem, UT (Broderbund CD-226):

Tyner, William W.

Dickerson, Mary Ann

Aug 7, 1845

Elbert Co.

2.  LDS.  Family Search: Internet Genealogy Service: IGI - International Genealogical Index (online at FamilySearch.org).

William W. TYNER Spouse: Mary Ann DICKERSON Marriage: 07 Aug 1845, Elbert, Georgia Source: Marriages, 1836-1913. Georgia. Court of Ordinary (Elbert County)

William W. TYNER Birth: 10 Jun 1818, Elbert, Georgia; Death: 10 Jun 1888, Madison, Georgia Burial: Jun 1888, Jones Chapel Methodist Church Cemetery, Madison, Georgia Marriage: 07 Aug 1845, Elbert, Georgia Spouse: Mary Ann DICKERSON Birth: 05 Nov 1817, Elbert, Georgia; Death: 04 Mar 1889, Madison, Georgia Burial: Mar 1899, Jones Chapel Methodist Church Cemetery, Madison, Georgia Source: patron submission

Thomas Callaway TYNER Birth: 02 May 1846, Elbert, Wilkes, Georgia; Death: 24 Dec 1912, Gainesville, Hall, Georgia Burial 1912, Calvery (sic) Baptist Church Cemetery, Gainesville, Hall, Georgia Rebecca Elizabeth TYNER Birth: About 1848, Elbert, Wilkes, Georgia R.J. TYNER Birth: About 1849, Elbert, Wilkes, Georgia Amanda TYNER Birth: About 1851, Elbert, Wilkes, Georgia John Chapel TYNER Birth: 25 Aug 1853, Elbert, Wilkes, Georgia; Death: 20 Jul 1923, Madison, Georgia Burial: Jul 1923, Jones Chapel Methodist Church Cemetery, Danielsville, Madison, Georgia Mary Cornelia TYNER Birth: 13 Jun 1855, Elbert, Wilkes, Georgia; Death: 05 Sep 1884, Madison, Georgia Burial: Sep 1884, Jones Chapel Methodist Church Cemetery, Danielsville, Madison, Georgia Benson William TYNER Birth: About 1857, Elbert, Wilkes, Georgia Tom TYNER Birth: About 1862, Elbert, Wilkes, Georgia William L. TYNER Birth: 14 Nov 1864, Elbert, Wilkes, Georgia; Death: 24 Nov 1941, Greenwood, South Carolina Burial: Nov 1941, Edgewood Cemetery, Greenwood, Greenwood, South Carolina Father: William W. TYNER; Mother: Mary Ann DICKERSON Source: patron submissions

There is no indication that their daughter, Elizabeth, had given name, Rebecca.  I suspect people were trying to turn the "R.J." in the 1850 census into Elizabeth, which is an error (R.J. is Reuben J.).  If our subjects had a son, Tom, born in 1862 (unlikely because they already had a surviving son named Thomas), he had to have died before 1870 because he is not with them in the 1870 census.  William L. TYNER is our subject's nephew, not his son (q.v.).

3.  1850 Census Every-Name-Index/Images (online at Ancestry.com, Image #139 of 160 [barely readable]; online at Genealogy.com, Image #139 fo 160 [readable]):  Elbert Dist. [the entire county is "Elbert Dist."], Elbert Co., GA, Roll M432_68, p. 433A, 1023/1023, enumerated 7 Oct 1850, official enumeration date 1 Jun 1850 (extracted by Diana Gale Matthiesen):

W Tinor	26	M		Farmer	500	Georgia
M Tinor	28	F				"
T C Tinor	4	M				"
R J Tinor	2	M				"
P Tinor	1	F				"

4.  1860 Census Every-Name-Index/Images (online at Ancestry.com, Image #144 of 153):  Carnesville P.O., Franklin Co., GA, Roll, p. 684, PN 144, 1037/1037, enumerated 8 Aug 1860, official enumeration date 1 Jun 1860 (extracted by Diana Gale Matthiesen):

Wm Tyner	41?	M		Farmer			Ga
Mary A "	40?	F		Domestic			"
Caloway  "	15	M					"
Reuben    "	12	M					"
Amanda P   "	11	F					"
Elizabeth J "	8	F					"
John C      "	7	M					"
Cornelia M  "	5	F					"
Benson W    "	4	M					"
Sarah F     "	3/12	F					"

5.  1870 Census Every-Name-Index/Images (online at Ancestry.com, Image #48 of 82):  Clayton P.O., Rabun Co., GA, Roll M593_171, p. 207B, PN 46, 318/325, enumerated 6 Aug 1870, official enumeration date 1 Jun 1870 (extracted by Diana Gale Matthiesen):

Tiner William	48	M	W	Farmer	500	1000	Georgia
_____ Mary	50	F	W	Keeping house			Do
_____ John	18	M	W	Farm laborer			Do
_____ Mary Panealius?	14	F	W	At home			Do
_____ William	12	M	W	Farm laborer			Do

6.  1880 Census Every-Name-Index/Images (online at Ancestry.com, Image #4 of 15):  Mill [Dist.], G.M. Dist. 438, Madison Co., GA, Roll 157, p. 83D, PN 28, SD 2, ED 74, enumerated 17 Jun 1880, official enumeration date 1 Jun 1880 (extracted by Diana Gale Matthiesen):

1880:  for an explanation of the column headings, please see What the Numbers in the Federal Census Mean (missing columns contained no data).
1	2	3	4	5	6	8	9	10	13	14	24	25	26
230	231	Tyner William W	W	M	63			/	Farmer	12	GA	GA	GA
		_____ Mary A	W	F	60	Wife		/	Keeping House	12	GA	GA	GA
		_____ Mary C	W	F	20	Dau	/		works in House	12	GA	GA	GA

This enumerator has all the adults on the page as "12" in Column 14.  I don't know where he got the idea that because you were a farmer (or a member of his household) you were unemployed!

7.  1890 Census:  the 1890 Census Population Schedules were destroyed.

8.  Georgia Deaths, 1914-1927 (online at FamilySearch.org):

Name:	W. B. Tyner
Death Date:	20 Nov 1921
Death Place:	Griffin, Spalding
Age at Death:	65 y
Estimated Birth Year:	1856
Birthplace:	Ga
Gender | Race:	Male | White
Race or Color:	White
Ethnicity:	American
Father's Name:	Don't know
Mother's Name:	Dickerson
Digital Folder:	4176958

9.  Public Member Trees (online at Ancestry.com).

10.  WorldConnect / Ancestry World Trees (online at RootsWeb.com/Ancestry.com).