Although there are other online die rollers that explicitly handle exploding dice, if you want to use Elliquiy's then the easiest thing is probably to just have the player roll a ton of extra dice every time they roll. Then read them in order, using as many additional dice as necessary to do your exploding.
For example, if you're doing Star Wars, and the roll is 3d6 plus an exploding Force die, you could put in 10d6.
If the results are:
1,2,6,3,4,5,5,2,2,6
Then you only need 1+2+6+3. The "3" is the Force Die, and since it's not a six it doesn't explode. Your total is 12 and you ignore the rest of the dice.
(1,2,6)(3)(4,5,5,2,2,6)
If the results are:
1,2,6,6,6,3,3,2,1,5
Then your regular dice are still 1+2+6. Your Force die is a 6, so you keep adding more dice from the list until you hit one that isn't 6. In this case 6+6+3. Your final total is 24.
(1,2,6)(6,6,3)(3,2,1,5)
The key here is to just say up front how you're going to read the dice and stick to it. Don't decide after you roll, and don't let the players use different systems. Otherwise you might end up with someone saying "that 6 in the first position, that's my Force Die", or something along those lines.