The line "Points from the arcanist reservoir are used to fuel many of the arcanist's powers. In addition, the arcanist can expend 1 point from her arcane reservoir as a free action whenever she casts an arcanist spell. If she does, she can choose to increase the caster level by 1 or increase the spell's DC by 1." comes from the arcanist reservoir section, not the arcanist exploit section. Further, the line does not specifically state you need to be casting an arcanist spell to access the arcanist reservoir, but gives you a generic use for the reservoir and that use is restricted to the arcanist spells.
The exploits section gives you a long list of abilities that tap into the reservoir that would take a standard or full round action (spell-like abilities) that would prohibit you from casting any sort of spell, arcanist or otherwise.
So, by design the two are separate: Arcane Reservoir and Arcane Exploit, and you don't need to be casting an arcane spell to use it. This means that an arcane exploit should be usable with other spell classes.
The better question is what happens when you do use arcane exploits with other spell classes? If we're talking about the metamixing feat you might have issues, especially with prepared caster classes. Spontaneous casters are considered to have free spell slots until they're used - they KNOW their spells and can use any spell in an appropriate slot without loosing use of that spell for the day, just the slot. Prepared casters are different - their spells are locked to specific slots when they prepare them. When you use metamixing you apply the meta-magic feat spontaneously without effecting casting time, but you still effect the spell level. For a spontaneous caster, this just eats up a higher level spell slot. For a prepared caster this would appear to eat up the original spell (in one slot) and burn a higher slot (an presumably the spell prepared in it). So... a prepared caster using this exploit would be eating up two of his spells per day to use this exploit.
And there in is your balancing agent that prevents this exploit from being super-powered. It's great for spontaneous casters as it gives them a more effective means of using metamagic feats - but they get slower access to higher level spell slots to tack those feats to. For prepared casters it burns two spells of different levels at the same time.
This is, at least, my interpretation of what is written.