A: No.

Andy says that the arrows going out from the Time Repair Agency are like a combination of the arrows on the tiles, and the Move card arrows.

Like the other tile arrows, you can choose to follow one as your turn action, without having to play a card. However, directionally, and with respect to the Wraps & Gaps rule, they are more like using a Move card, so you would jump over missing tiles as if you’d moved horizontally or vertically, rather than being bounced back to TRA as if you’d landed on them out of nowhere from another timeline tile arrow.