OK, looks we should go though the basics - I`m trying to explain again and go through the details.
What you want is basically a limited influence of a modifier. You can consider explosia object being a modifier like others, e.g. xpturbulence.
Do do so, xparticles has groups. You can think of a group as a container where specified particles are in and you can limit modifiers´s forces to act only on specified groups by dragging group objects into the window found in groups affected tab. This way Explosia has this window as well to be found under the advection tab , just called groups.
So lets go to through the scene you attached above again in detail.
First things to do - disable emitter called plane as it´s output hides things we want to see and delete animation for activating explosia, we don´t need that at all.
Now go to texture emitter -> display and set it from dots to box or circle for better visualisation, let´s say box. If we play animation now, some white boxes are coming towards us, not what we want. Tried to change your texture that I get an alpha, but had to realize, that does not work, not sure if bug or limitation. So most simple solution - don´t use a plane but a disc for emission. and apply texture to this disk. In texture emitter all you have to do is replace object emitter plane by this disk. Now we have particles from white areas emitted , again not yet what we need.
Time to explore texture emitter´s texture settings. Go to texture emitter -> texture tab and as a first step we are going to disable all channels by setting everything from colour to none.
Now we get green particles emitted from the disk as none of the texture channels is evaluated. You may now try and activate emission channel by setting this from none to colour. Now you see our green particles are emitted from white areas only, not what we want so set this to none again as I explained in my previous answer . This channel is working as a limiter for output rate , white full output, black none.
Time to introduce groups as long as we get visual reference. So go to texture emitter -> groups tab and click create and add group. As the group is active now, just change the colour to anything, let´s say green ( which it might be already depending on some preference settings). Nothing changed so far as we play animation now.
Repeat that step and in texture emitter create and add another group and change it´s colour to anything else, maybe red.
If you play now, you have red and green particles coming from the disk, but randomly distributed and not from texture colours as you want. If you cycle through the mode options within group tab, you´ll find nothing you can use directly, random, sequential, use gradient ,everything is meant for particle index, so you have to choose "use first group only" and we take care for sorting later. Now all particles born are within group 1 and we can go to explosia , advection tab, activate this again ( got lost when we deleted animation) an drag group 2 object to the group window.
If you play now - nothing happens as all particles are emitted to group 1 so this group explosia is limited to use is empty now, nothing to advect. We have to send particles to be affected to this group. Let´s see how we can do that now,
First step, back to texture emitter , we go to object -> texture tab and set colour channel from none to colour. Now playing animation we get white particles from white areas and black particles from black areas - that´s a step further, but still all particles are in group 1, so nothing else happens. But now we have an additional tool, xparticle´s question /action options.
We can go now to texture emitter´s questions tab and add a question , it adds as a default asking for age, not what we need, so we change this to colour, just next option on particle data cycle list. Default is set RGB value greater than 128,128,128 so just what we need as we want to send our white particles that have close to 255,255,255 - sure with a variation as it gets values from the texture colour at the position where this particle has been born . As an action (-> add action) we choose action type -> direct action and direct actions -> change group.
New group is group 2 of course and groups affected you may drag in group 1.
Now we are almost there. We see black and red particles coming and the red are moving according to advection now as group 2 is filled with all particles that are emitted from white areas now.
We don´t want the particles to turn red (the group colour) so all we have to do is in change group action, uncheck colour, so the original colour is kept.
Now you should see black particles coming in straight and white particles in a chaotic motion caused by advection as you desired ...
Hopefully everything is clear and understandable now.
As a last point to consider, once you limit a modifier to a group, it will ignore all other particles. So does explosia. If you want the other particle layer from emitter plane we switched off as a first step be affected by explosia as well, you have to create a group in it´s group tab as well and drag this group to explosia -> advection group window . Without that group, this emitter activated again will be ignored by explosia...