Technically, Initiative, Astral Initiative and Matrix Initiative are 3 separate entities and your Initiative modifiers would then not work on the other two. So with that difference explicitly made in tables, it sounds like a set of Wired Reflexes won't make a Decker faster, and the Increase/Improved Reflexes spell/power sound like they won't help astrally.
The initiatives types are broken down into types on page 159. The table lists 6 types (with no mention of VR Rigging), but the paragraph breaks it down into 4 types: Physical, Astral, Matrix, and Rigging. By your logic, you'll need separate initiative modifiers for physical combat and AR Rigging and AR Matrix hacking which is explicitly not the case as described in the augment reality user mode on page 229.
Additionally, the increase reflexes spell does not specify an initiative type. Wired reflexes and the adept power also do not specify an initiative type. It's left to the reader to infer under which scenarios which dice apply. I thought that the astral world section would specify restrictions, but it only implies them in the form of replacement attributes on page 314.
You have EARS (sp?) from a recent book that lets you use your Matrix VR initiative for physical actions (with penalties and there may be restrictions). When you have a dual natured entity (such as an astrally perceiving character) fighting on the astral, the character will be using physical initiative against astral foes using astral initiative. Control rigs don't help with initiative anymore?
Finally, the cold sim VR user mode description (page 229) reiterates the +5D6 initiative limit when describing that it gives +3D6 initiative, implying that there is another source of applicable initiative modifiers. I cannot think of any other than augmentations and magic, but maybe I am overlooking something.
Only mana spells work in astral. So combat sense yes, increase reflexes no. From the CRB under the astral combat section:
"There are no ranged weapons that function in astral space, so unarmed attacks, active weapon foci, and mana spells are the only options for astral combat.".
Even though the skill used is astral combat in place of the normal weapon skill, unarmed attacks and weapon foci attacks are still very much a melee attack. Combat sense would work just fine.
A reference not limited to combat spells would be:
Only mana-based spells work in astral space, even if you're in the physical world astrally perceiving the target.
As an aside, I can't recall anywhere that it specifies whether Adept Powers are "physical" or "mana," but I also can't think of a scenario where an adept/mystic adept would be in astrally projecting in astral space. There is the astral gateway, but if I recall correctly, that only takes you to the metaplanes. Do astral initiative rules apply to the Metaplanes?