Inbound after made basket/timeout

[CoachP]

Team A scores and just as B1 gets ready to throw in, I (Coach B) request a TO because team A is setting up a full court press.

There is confusion among my players after the TO as to who the inbounder is and the Official places the ball on the floor and begins the 5 second count.

B1 manages to get OOB and pick up the ball for the throw in. Even though the ball was placed on the floor, B1 still has the right to run the endline, correct?

Should the official wave his arm along the baseline after setting the ball down? (indicating B1 could run the baseline)

We were at fault I admit, but after 1 request for an inbounder, was he a little too quick to set the ball down?