Latency compensation in most DAWs works based on reported latency by the interface. Specs of the computer have nothing to do with it except for preventing buffer over/underruns.
The way it works is this: when the DAW is in playback mode, you hear whatever real latency is there via the live (e.g. monitored through the DAW) armed tracks.
So, e.g. for rehearsal, you’ll get a few ms or so of latency (double the single-path latency figure shown for your interface and buffer combination) hearing yourself play along with the audio, but that’s usually (on a modern system with 4-8ms of one-way latency) tolerable (except in a few cases for drummers with an exceptionally tight sensitivity to timing). It’s roughly the same as hearing yourself in the monitors on a largeish stage.
But when the DAW goes into record mode, you hear the same thing, but when it puts the audio on the timeline, it subtracts the one-way latency from the input signal, shifting it “back” in time by this figure. This, in most cases, with most interfaces, puts it bang on timing-wise with the rest of the recorded tracks.
This is if latency compensation (the manual adjustment figure) is 0. If you put ANYTHING in that figure, it’s added or subtracted from the automatic compensation. In other words, unless the automatic compensation is flat out wrong (usually due to poor driver design or crappy audio hardware - not the case with RME, later MOTU, etc. gear), you should have nothing in this field at all.
As @jonatron said, if you have anything else in the signal path (external audio effects, for instance) that add latency to what ultimately ends up on the track, you could be shifting this value - but that would only apply to the audio either coming OFF the recorded track or the audio going IN (which you would hear, and thus somewhat compensate for by your playing style). It will still be lined up on the recorded track as it would have been without the buffer in the way.
This is where direct monitoring comes in - if you’re monitoring through the DAW, you may be overcompensating in your playing for the perceived latency and thus playing too early. This will result in your recorded track appearing “early” compared to the other laid down tracks too. If you’re monitoring direct, you won’t hear any difference between the playback and your playing, and the DAW will make only it’s automatic compensation for the buffers and interface timing, and things should be quite close to sample accurate once you play back what you recorded.
If you’re seeing your recorded track coming in LATE comparatively, then you’re either playing behind, or you’ve put an incorrect latency compensation value in your tracks, or your interface is really badly mis-communicating the latency to the DAW.
My recommendation: apply no latency compensation manually, use automatic latency compensation if it’s an option in your DAW, and record using live (direct) monitoring, with the DAW input monitoring OFF. This leads to the most accurate physical timing as well as the most correct placement of the audio on the recorded track relative to the other tracks.
