I may have been looking at the TDS for 7950SP. Do whatever the instructions for the product you have says to do, within reason. Most end-users won't have custom laser-cut stencils, so a more simplistic tape square, or a much less precise manual spread will have to suffice. Applying heat (don't blow directly at the TIM, heat the object from the opposite side, use IR, or put in a higher temp ambient) is almost certainly an option to dry it faster.
Interesting, and not surprising. The thermally conductive component of any paste is the filler...the binders or solvents that make them liquid are only there to make sure they can be applied and that they fill small enough voids. A phase change material doesn't need or benefit from the later as it's phase change properties take care of that.
It's not a normal paste, it's the paste form of a phase change material. If it's solid phase wasn't solid/dry most of the benefits would be lost. And if those benefits were possible in normal pastes without downsides like drying time and more limited storage life, normal pastes would all be like this.
The material is formulated to be stenciled on with a squeegee, so is quite low viscosity when fresh, and recommended pot life for the paste, once opened, is very low. It's very possible that the tube you had was older, was stored differently, and didn't need as much time for what was left of the solvent to evaporate. I'm not even sure tube-size formats are officially supported by Honeywell and probably imply quite a bit of solvent loss simply in the process of someone pouring them into a tube.
The remaining solvent would surely evaporate and escape during thermal cycling, but might not leave the TIM interface exactly as expected. It's possible you'd see some improvement with a new application. Probably not worth redoing, unless you encounter issues at some point. As always, there is margin for error, but ideally, PCM is dry before mounting the cooler.
You likely have the standard PTM7950 pads, which are essentially a pre-dried version of the paste. The plastic is just there to hold it together and protect it before application.
There is probably a non-SP version of PTM7958, but as it's a semi-custom version of 7950 made for OEMs, I haven't seen the pad version and the paste version would be more useful to an OEM that is stenciling their own patterns for their own hardware.