So, I was re-watching Raiders of the Lost Ark last night, and something about the beginning bothered me. When Indy gets in the plane, he's beset upon by a giant snake. He flips out about this, yelling to Jock that he hates snakes. But, if Jock flew him there, wouldn't he have known about the snake? So, how did Indy get there to begin with? And if he didn't fly with Jock, why not leave the same way?
It's not clear from the script (or the official novelisation or the comic-book conversion) how Indy actually got to the temple. It's pretty clear that he's traveling with two companions and that he (or they) somehow made contact with the locals before traveling to the jungle temple. The plane is certainly waiting for him, but there's no special indication that he used it for the outward journey, especially given that they've got mules and supplies.
Given that the plane is a two-seater it's very possible that Jock and his plane were chartered only for the return journey which would explain why Indy hadn't encountered Reggie before.
Failing that, it's reasonable to assume that Jock (who evidently wasn't expecting Indy to return so soon) had released Reggie from a bag or from under his own seat into the plane's second seat. He may have planned to return him to his bag except that they had to take off in a hurry.