Like the title says, just how do aspected domains work with spirits? Street Magic (pgs 118-119) says an aspected domain gives a magician who is aligned with that domain a dice pool boost to any magical skill tests and drain tests.
Spirits don't usually make either of those sort of tests so what effect does an aspected domain have on a spirit?

Imagine a free spirit with the spellcasting skill and tremble.

Regular old spirits are mostly unaffected, but there may be a few exceptions depending on powers.

Never forget that a Spirit not of the aspected Tradtion loses Magic/Force equal to the Domain Value. It is a great way to make sure that non-aligned spirits are weaker when in your domain and aligned spirits more powerful. In 4th Edition, they do not suffer DP Penalties... they suffer Magic/Force Penalties just like Spells/Foci do.

I'm less concerned about the negative aspects of a domain. The issue that came up dealt with aligned spirits. It seems, at least according to rules as written, that an aligned spirit in an aspected domain has no real effect unless that spirit can cast spells. Is this the intention?

Obviously hard to tell, but it would be a sensible balancing decision: The mage can already call a larger spirit than usual while inside the Domain, if that spirit would also get the Domain bonus to its actions, the bonus was basically granted twice.

That is still a different application of the bonus, though Sengir...
Mage getting the bonus for his actions is not the same as the Spirit getting the bonus.
I would argue that since the Spirits suffer the penalty if unaligned to the domain, then they should get the bonus if the are aligned to the domain.
But its been a few years since I played SR4, so... no real dog in the fight.