Even though your play at any mlife property will accrue tier credits and will be used for corporate offers, if you dilute your play across too many properties, it will affect future property specific offers resulting in smaller comps - it might not affect it by much for just one trip; they may also look at history. Each property evaluates your play at that property during your stay in consideration of back end comps and future offers for that specific property.
So say, for example, your total coin in overall is a large amount but spread across four properties and say you even earned gold tier status through your total play. The property where you are staying is only going to evaluate your actual play at that property in regards to potential back end comps and future property specific offers - regardless of tier status. Also, it takes considerably more play/coin in at higher end hotels like
Aria and
Bellagio to get an offer similar to what you will get at
NYNY or
Luxor for that same play. (That is my opinion based on my experience and I will stand corrected if others have better more specific information). I am Platinum at mlife and my offers at Mirage and
Mandalay Bay are a little better than my
Aria and
Bellagio offers. I have even better offers of FP and RC at
NYNY,
Luxor, Excal - places I have not yet stayed at...
Hope this doesn't muddy the waters