The only time I've come across this is when one or more tracks is sidechained to the kick, precisely in order to get this 'pumping' effect. It's called 'ducking' and it's a main feature of EDM. But you have to set it up manually. Even if you had a compressor on each track by default, it would still have to be manually sidechained in order to have that effect.
You don't need either the multiband dynamics tool or the compressor just to make a track louder. You can either increase the gain using the track's fader, or you can put a Utility at the end of the effects chain on the track. The latter way of doing it has the benefit that you can automate the gain throughout the track but still leave the main fader free for mixing and mastering after you've done all of your tracking. I do this all the time and my default tracks have an EQ8 and a Utility on them. So I can fit each track into the mix according to frequency and panning, while doing gain staging as I go.
If you have drums or vocals (or anything else) where some parts of the track are quieter than others, you can use a compressor to even things out. The way it works is to reduce the loud sounds to bring them down closer to the quieter sounds. You can then use makeup gain to bring the gain back up to where it was before the compressor kicks in. If you're mixing several different drum loops, patches, or samples, the Glue Compressor is great for making everything fit together nicely; ditto with, say, a bass and sub-bass. And the normal compressor works well with vocals.
Another good use of the compressor with drums, and especially the kick, is to bring out the transient. By playing with the attack and release controls, you can get a loud transient at the start of the sound followed by a quieter 'body' to the sound. And, of course, you can use a compressor to do the opposite - to bring the whole kick sound up to the same volume throughout.
How do you do all this without destroying the mix? It depends on the style of music. With EDM I would set the kick(s) up to maybe -8dB (my preferred maximum) then bring the gain up on the bass until it fits nicely with the kick. Then I'd bring up the rest of the drums and the other tracks to suit. With a song, I'd start with the vocals hitting the maximum -8dB then bring in the kick, drums, and bass so that the vocals can still be heard clearly. When bringing in the other instruments, I'd 'sculpt' the frequencies using EQ8 so that they don't overwhelm the vocals. Orchestral style music is a little different in that it doesn't have the driving rhythm section, so panning and EQ are as essential to get right as gain staging. But, since you mention the kick, I assume you're not creating an in-the-box orchestra. If you say which styles you are working with, I'm sure someone can point you to some more useful advice.
So, to sum up, if you haven't set up sidechaining explicitly, I have no idea what might be causing your pumping sound. Could it be a 'feature' of your sound card or speakers?
