If I counterstrike on Stellacorn, at the end of combat if we tie, is it a "move" for me to return to base when the attacker goes back?

No, it is not considered a "move."

According to Rule 450 and established RiftJudge FAQs (specifically FAQ #9617 and FAQ #10124), returning to base after failing to conquer a battlefield—regardless of whether that return is caused by combat results or tied combat—is defined as a Recall.

A Recall is explicitly distinct from a Move in Riftbound. Because Stellacorn Herder’s ability ("When I move, draw 1") specifically triggers only upon a Move action, it will not trigger when your unit returns to base via a recall after the combat ends.

Summary of Combat and Timing:

1. Counter Strike: When you played Counter Strike, it resolved (preventing damage and drawing you a card). This effect persists for the turn.
2. Combat Resolution: After combat damage and the combat cleanup steps, if both players have units remaining or neither player has units remaining (a "No Result"), a recall occurs to clear the battlefield of attackers if defenders remain (Rule 461.1.a.2).
3. The Trigger: Because this return to base is a Recall (Rule 450) and not a Move (Rule 144), the "When I move" condition of Stellacorn Herder is not met.