Uninvited guests.

Taking damage before the archers’ turn is normal for humans.

Absolutely. If it were very similar to the standard version, there would be nothing to write about. But…

dividing the archers into 2 stacks.

cannot change anything (just like dividing into a larger number of stacks); both groups will end up at the end of the turn order, and they will shoot after all the enemy stacks. In the normal version, there is a possibility of alternating turns between groups or even pushing your own units with lower initiative ahead: for example, overtaking druids with 10 initiative (against 8) at the start. With Rupert’s archers, this trick doesn’t work; they will definitely take damage from all groups.

if you equip them with artifacts that increase initiative.

It doesn’t help. The archers will still be at the back, only with a higher initiative. I equipped them with a Ring of Dragons, and none of the stacks (out of 3) started moving before the Cave Lords. In the normal case, there should be an alternating pattern, with the first turn of one of the archer stacks.
The presence of a tent, magic – this is already a different level of hero development and a significant complication of the battles with neutrals, shifting them to a later stage of the game. That is, the tasks that previously required only the interaction of your own stacks or a suitable artifact are now solved through the acquisition of schools and perks from them.
The low starting initiative of the archers is very unfortunate, and most importantly, it’s inescapable; it needs to be removed.