Okay this is a strange one. When a tumor familiar is attached it is considered part of your body. Does that work both ways; are you considered part of it's body?
I ask this because of improved familiars having spells that target self only. Everything in me screams that this should not work both ways and I wouldn't allow it in a game that I was running without an official ruling on it.
What I have found so far only supports that it should indeed be a two way street. If I cast invisibility on myself the tumor becomes invisible. So when the tumor cast invisibility on itself I should also turn invisible.
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Tumor Familiar (Ex) (Ultimate Magic pg. 1 (Amazon)): The alchemist creates a Diminutive or Tiny tumor on his body, usually on his back or stomach. As a standard action, the alchemist can have the tumor detach itself from his body as a separate creature vaguely resembling a kind of animal suitable for a familiar (bat, cat, and so on) and move about as if it were an independent creature. The tumor can reattach itself to the alchemist as a standard action. The tumor has all the abilities of the animal it resembles (for example, a batlike tumor can fly) and familiar abilities based on the alchemist’s caster level (though some familiar abilities may be useless to an alchemist). The tumor acts as the alchemist’s familiar whether attached or separated (providing a skill bonus, the Alertness feat, and so on). When attached to the alchemist, the tumor has fast healing 5. An alchemist’s extracts and mutagens are considered spells for the purposes of familiar abilities like share spells and deliver touch spells. If a tumor familiar is lost or dies, it can be replaced 1 week later through a specialized procedure that costs 200 gp per alchemist level. The ritual takes 8 hours to complete.
Oneyou has it right. The relevant text should indicate the tumor cannot even detach itself, the alchemist has to use the action to do so.
There's nothing in that text that supports your theory that it ceases to be a creature when it attaches itself.
No: if it is an independent creature capable of its own actions (using a SLA), then the alchemist is not part of its body and does not benefit from such things as At Will Invisibility.
Wait, so if an attached tumor familiar is an independent creature with its own actions, can it also be targeted separately by attacks?
It could all use some clarifying text, but Die for your Master makes it fairly clear the intention is for the familiar to still be a creature, capable of immediate actions, while attached.
As long as we're looking for clarifications, the interaction with the Protector familiar archetype and relevant powercheese should be addressed, as well.
The Die for Your Master feat is not evidence that the tumor familiar can take independent actions while attached (rather the opposite in my opinion). Taking a feat (the master takes the feat) grants the tumor familiar the ability to, under very specific conditions (I.e. about to take lethal damage from a blow in combat, not even trap damage), shift physical location and absorb some of the damage.
A better example of how to treat it is the Tattoo Sorcerer and the tattoo familiar.
If it was an independent creature, it would be targetable by spells and melee attacks as well as taking damage or suffering the effects of area of effect spells and abilities.
However, back to the original actual question, the master is not affected by an improved tumor familiar's SLAs because of either condition:
No. The tumor is not an independent creature and thus cannot take action.
No. The tumor is independent and thus not part of the master's body.
I interpreted that as "serves as the alchemist's familiar," meaning you still have the Alertness feat and the familiar bonus even in tumor form.