Tillman was drafted by the Mets in the 10th round of the 1979 amateur draft out of Florida Community College at Jacksonville, and he began his professional career that year. He played for the Grays Harbor Loggers and Little Falls Mets, hitting a combined .297 with 23 stolen bases in 66 games. In 1980, he played for the Lynchburg Mets, hitting .316 with 11 triples and 43 stolen bases. With the Jackson Mets in 1981, he hit .278 with 29 stolen bases.
