Thanks for the extra details. Makes it much easier to address your question. Now what you read on LoopTV isn't wrong, but phase alignment is just 1/3 of the equation. I'll explain...
[b]1. Coincident Volume Envelopes[/b]
Depending on your zoom level, you'll see different things. In this view we see kind of an "overall shape" of the way the volume fluctuates in a piece of recorded audio. This is called the [b]volume envelope[/b].
At this zoom level we can't see detail along the horizontal axis (left to right). We can only really see detail ("ish") along the vertical axis (volume envelope). This is still a useful view of things, because you can definitely get a feel for whether or not the peaks of the volume envelopes of multiple kicks, say, are in line with one another. This is what's referred to as phase alignment. If the peaks aren't phase aligned in this way, the sound could get smeary, or in extreme cases, they'd sound like they're flamming.
An important aspect of phase alignment is making sure that the peaks are all pointing in the same direction, and preferably "up" (in the positive direction). When the peaks of, say, two kick drums are aligned [i]and[/i] pointing in the same direction, their peaks will reinforce one another sonically -- volume-wise. If one kick's peak was inverted (peaking downward) then the volume energy from one kick will subtract from the other one. That's a kind of [b]phase cancellation[/b]. There are two kinds: volume cancellation, and frequency cancellation. I'm just about to get to frequency...
[b]2. Frequency Considerations.[/b]
What we can't see along the horizontal axis at more zoomed-out zoom levels is the frequency of the kick waveforms.
Not that I've ever known anyone to get so crazy as to try and tune multiple kicks so that their frequencies are the same (pretty much an impossible task anyway) but here's the point: the frequencies (pitches) of the kicks have to be just right in order for them not to cancel one another out, reinforce one another (in a sonically undesirable way), or beat with one another. So the choice of which kicks you're going to combine really has to be done by ear. Phase aligning them so that their peaks are coincident is an important step towards getting a cohesive kick sound from multiple kicks, but there's no guarantee that they'll combine nicely due to their frequency content. Sometimes it's possible, other times it's not.
So if you want to combine the flavor of several kicks, know right from the start that you're not always going to bat 1000 even if the kicks are aligned.
And that brings me to...
[b]3. Relative Volume and Fudge Factor[/b]
When combining multiple kicks, one of them should always be the "main" kick, with the others adding some kind of flavor. If you combine multiple kicks and you just can't get them to sing nicely together, try reducing the volume of the "flavor" kicks. There's nothing scientific about this approach other than using your ear to try and make something sound good that's not otherwise working.
The idea of "fudge factor" is that phase aligning kicks may not produce the most desirable result after all! You may find that advancing (or delaying) the sound of the "flavor kicks" by a tick or two will suddenly cause those kicks to blend.
So yes, indeed, try to get multiple kicks, claps, and snares to be phase aligned in terms of their volume envelopes. But if you find that the sound isn't working, start employing the "fudge factor", using your ear as your guide to get the sound you want.