...a second listen

The mat is a pretty important part of the turntable! It controls resonance in the vinyl caused by the tracking of the cartridge. If not controlled, the resonance can talk back to the needle and so mess up the sound.

The proper mat will be of the same hardness as the LP itself, so as to prevent any reflections of energy at any frequency. So they can affect the tonality!! No mat at all will be too bright and a soft mat like felt or leather will be too soft (and some oils will be imparted to the LP surface, allowing it to gather dust a lot easier). Felt mats are only used by DJs to act as a clutch between the platter and the LP surface. Mats of this latter type are not predicable sound-wise- they might also be bright and trashy, simply because damping is almost non-existent.

A good mat will also serve to damp the platter to some extent. This is a lot to ask of a mat which is why its a good idea for the platter be damped on its own. Two mats that I favor are the one made by Oracle and the Vibro Stop. I'm sure there are others but when examining the issue keep the principles I've outlined above and you will save yourself some cash.

is that across the board with all tables?

Yes. The problem is finding a mat that is neutral. Obviously a lot of them cause more problems than they solve so no mat at all might be preferable in some cases.

How do your findings relate to a tt with a vacuum sealing function?

Getting the LP to be flat really increases the effect of the mat and also reduces the amplifier power used since there will be less warp. The flip side if you will pardon the expression is damage that might occur to the other side of the LP. I've seen some vacuum systems do serious damage to the unplayed side.

On my Oracle I use the original IsoGroove. Were you referring to this or their new acrylic mat?

We've been getting the same mat from them for the last 15 years so I'm going with the former rather than the latter.