Thanks for the report. I looked into it. Send Pet shouldn't move you: your pet goes and you stay put. In the server log for your fights, each time you sent your spider, a Shield Charge from you followed a few seconds later, and a charge runs you straight at the target. Could that be the walk you saw? If you're sure you didn't press Shield Charge, let me know what you tapped and roughly when, and I'll keep digging.
Also coming in the next update: you'll be able to send your pet and Golems at other players, not just creatures.