At the time of Griffith's Valuation in County Tyrone, George Latimer/Lattimer held land in Tullahoge townland, Desertcreat parish (ancient dynastic seat of the O'Neills), and in Killeen, Clonoe parish. Griffith's doesn't state if this is the same man or different men, but full details of each property entry (did one man have house and land, and the other just land? Very likely the same man) combined with other records might show you.
You already know that your ancestor William Latimer married in the Newmills Presbyterian church in 1878. Witnesses to the marriage might include relatives, so you should research those people as well as the bride and groom's fathers as named in the marriage record. William's residence at time of marriage should also be on that record: where was he living in 1878? Another clue to further background and relatives.
Presbyterian churches not far from Newmills that the Latimers might also have attended include Carland and Dungannon (Drumglass parish) and Stewartstown (Donaghenry parish). Any of those church registers might have more on your Latimers, as might the Church of Ireland registers. Tullyniskan parish Church of Ireland records date back to 1794.
If William Latimer's 1852 birth year is approximate, such as from a U.S. or Canadian census, his father might be the "George Latimer" whomarried Elizabeth Leonard on Oct. 21, 1852 at Clonoe parish Church of Ireland (listed in civil registration indexes). A son William could have been born the following year.