In Robert Stockdale's Dorsey Brothers book, the author says that Jimmy joined the Whiteman orchestra "sometime in late April, 1927" (without citing a source).
The following report confirms this:
Morning Telegraph, Monday, April 25, 1927, p.14
Jimmie Dorsey, once with Lopez, will be in the Paul Whiteman tiers this week, drawing weeps with his blue clarinet and sax.
"This week" would have been April 25 - April 30.