Doing some research, and trying to find out for certain if these two knew each other. Tillinghast designed Fresh Meadow in 1922/23, and 23 year old Sarazen (with three majors under his belt) was first pro in 1925, but I so far have no evidence that they knew each other. Its been opined that Tillie might have recommended Sarazen for the job, but no proof. For the 1932 US Open at Fresh Meadow, Sarazen resigned as pro so as not to jinx his chances (it worked), and Tillinghast was in attendance, so its likely they met, but no proof. Sarazen got his start at Brooklawn in 1916 and Tillinghast was brought there in 1929, possibly recommended by Sarazen, but no proof. Tillinghast didn't play tournament golf after 1915, so they likely never played together competitively.
If anyone has anything interesting, please jump in!