Green’s Dictionary of Slang

badly timed, at the wrong time, therefore unacceptable; by ext., unfashionable.

1943		Chicago Trib. Graphic Section 26 Dec. 7/1: Jive Talk [...] Off-time jive — a poor excuse, saying the wrong thing.
1944		Cab Calloway New Hepsters Dict. in Calloway (1976) 258: off-time jive (n.): a sorry excuse, saying the wrong thing.
1946		Mezzrow & Wolfe Really the Blues 217: Man, just look at him, dig that vine all offtime.