[smurfgirl]

Human players can throw game pieces (except supercells) in during autonomous without penalty. From the Q&A, posted by the GDC:

There is nothing in the rules that prohibit the Payload Spec1alists from throwing Moon Rocks during Autonomous.

The autonomous period ends when the clock reaches 0 for autonomous, from section 7:

7.3.2
Game Periods
<G01>
AUTONOMOUS PERIOD - The AUTONOMOUS PERIOD is the 15-second period at the start of the MATCH. PILOT control of the ROBOT is not permitted at this time. During this period, the ROBOTS may react only to sensor inputs and commands programmed into the onboard control system. All ROBOT safety rules are still applicable during the AUTONOMOUS PERIOD. The AUTONOMOUS PERIOD ends when the arena timer displays zero seconds left in the period.

This means the drivers can step forward at this time.

The teleoperated period begins just after the autonomous period ends- from section 7:

<G02>
TELEOPERATED PERIOD – The TELEOPERATED PERIOD is the 2-minute period of game play immediately following the AUTONOMOUS PERIOD. At the beginning of the TELEOPERATED PERIOD the OPERATOR CONSOLE controls are activated and PILOTS may remotely control their ROBOTS. The PILOTS continue to teleoperate their ROBOTS for the remainder of the MATCH. The TELEOPERATED PERIOD ends when the arena timer displays zero seconds. This also indicates the end of the MATCH.

Immediately implies that there is no delay. Also, if the teleoperated period begins immediately, the payload specialists can just continue to throw game pieces, as they are allowed for the duration of the match.


Edit: In response to,

And finally, what would happen with those 'airballs' that have been thrown before the buzzer, but score afterwards?

If you are talking about bell signaling the beginning of teleop (=end of autonomous), it makes no difference, because the game simply continues.

If you're talking about the end of the match, from section 7:

<G07>
Scores are determined based on the state of the GAME PIECES at the end of the MATCH.

And from above, the match ends when the clock hits 0, so a ball which falls into a trailer after the clock hits 0 will not count. (Often they later add a clause that scoring is done when all the game pieces have come to their final resting state or the like, so you might want to wait to see if this happens.)