Givens flatly states that Davis "went to Matamoros to organize the First Texas Cavalry, U.S.A., made up of Unionists like himself." Later, Jackson and others are captured by the Rebels in a cross-border raid into Matamoros.
It is hard to come by references to organizing in or operating out of Matamoros in other sources. A website dedicated to Texas politics has Davis receiving his colonel's commission from Lincoln in Washington May '62; the next geographic reference is Galveston.
The Civil War Archive website gives what appears to be a summary "official" history of the regiment citing an organization date in November of '62 in New Orleans. The Handbook of Texas online follows this convention but tantalizingly adds a quote, "the strength of the Texas Federal Regiments consisted primarily of Mexicans, Germans, and Irishmen."
The blogger Screwtape has some rich tidbits about Davis's late war career but nothing on Matamoros adventures.
Was Matamoros a base of operations for Unionists?
Update. Will Keene writes
There are multiple references to this in the ORs. As an example, look in Series I volume 15, page 1016 at correspondence dated March 15, 1863 from H.P. Bee, the confederate commander on the Texas side of the Rio Grande. Also see letter from Magruder to Cooper on page 1030.Excellent. I'll do a little legwork and report back.
(Show above, Davis and Matamoros in 1864).