I suspect this is your Jesse's family.The census was taken in January and since he was born in February, 1920, he wouldn't have been listed.
1920 McNairy Co., TN: Thomas W. Tidwell, age 52, b. TN, parents b. TN, farmer Emma, age 39 (probably 2nd wife), b. TN, parents b. TN Horace O., age 24, b. TN Fratie D. (son), age 14, b. TN John M., age 12, b. TN Artie M., dtr., age 8, b. TN Hurley L., son, age 5, b. TN
This same Tom/Thomas was in McNairy Co. in 1910 and 1900. Then I think this is his family in 1880, still in McNairy:
J.W. Tidwell, Jr., age 25, b. TN Martha, age 20 A.C., dtr., age 2 Harriet, age 7 Thom. W., age 5
Next door is John Tidwell, age 63, wife Elizabeth, age 57, probably J.W.'s parents.
I haven't had a chance to check 1930, but Jesse should be there with the Thomas W. Tidwell family.