You can test it even easier with Web. This is how it works, and has been for a while.
Worth noting that there was a point in the game’s history where all summons came in at the arena cap (level 15), but that was “fixed” long before the recent revamp so it was likely considered a bug (I found the original “bug report” with some people stating at the time this was working as intended, but then later that it didn’t work like that, but couldn’t find the official word or when it changed).
The problem with a lot of other summoning troops in arena (not Sunbird here) is not just that they have to rely on magic stats but also that at some point in the game’s history the devs inexplicably stopped giving base magic to summoners that didn’t have another effect that scaled off magic. This is a double-whammy to troops with a dedicated summoner role - not only do they not have an additional scaling effect but because they don’t, they can’t even summon effectively. For example, The Infernal Machine has a base magic of 0 regardless of level, even though it relies on magic to summon, because it doesn’t have other components that scale with magic. Even worse for something like Fel Dragon Egg. Compare to something like Kobra, which has a base magic of 12 at level 20 (7 at level 15, damage is +4 with a potential boost ratio, while not easy to set up in the arena, and can summon 1 or 2 troops). If you want a more recent example, look to Book of Secrets, which has a base magic value because it has a different spell component that scales off magic.
This isn’t a rarity thing either, and it isn’t just limited to troops introduced in delves (eg., Queen Moonclaw versus any of the many legendaries introduced both before and after that deal damage and also summon). Its almost as if at some point whoever was in charge of assigning base level 1-20 stat spreads forgot that magic scaling is actually present for summons before you have piles of stat bonuses.
Edit: I say they started doing this after a certain point because very clearly old troops that only summon have their full magic scores, and in these days they generally had higher magic scores than their non-summoning counterparts, eg., Giant Spider, with a base magic of 17 at level 20. It didn’t seem like a conscious decision to double-nerf troops with a primary role of summoner in recent times, more likely an oversight.
So yes, the way magic works in arena as regards to summon is probably working as intended, including Sunbird issue in original post. But some other summoning troops are straight up missing their base magic, likely due to an oversight.