When more than one permanent enters the battlefield, transforms, becomes equipped, etc., timestamps are determined by each player in APNAP order. Arena does not appear to have an interface to handle manually setting the order.

This is rarely relevant, but take for example Blood Moon and Harbinger of the Seas. Each card tries to set the land type of nonbasics to a different type. If both cards were to enter at the same time (e.g. if they were both exiled under the same enchantment by Calix), Arena does not currently allow for the owner of the cards to decide which land type nonbasics should be.

I tried this in Full Control mode with all "Auto Order" gameplay settings turned off. In every scenario I tried, Arena decided Harbinger had the latest timestamp and made everything Islands without any input from me.