Hi Chomdo, does this look like your filter...
Emaux V650 sand filter | Free Freight | Monarch Ecopure F25 | Zodiac Titan Z650 sand filters | Brisbane | Gold Coast | Sunshine coast.
If so, it's the same as my Zodiac. Is it filter sand you're seeing in the pool? It's sounding like a displaced, unseated or broken lateral.
At the bottom of the filter are several "laterals" which are small pipes arranged like the spokes of a wheel. These have slots in them too small for the sand, so the sand stays in the filter, and only water comes back to the pool. If a lateral is not installed correctly into the receiver, or if a lateral is cracked or broken, some sand can get past and into the return pipes. This thread includes a full tutorial on how a sand filter works:
Deep Cleaning a Sand Filter
It's also possible that the sand got into the riser pipe during construction. That sand should have been flushed out the backwash during rinsing, but if it wasn't rinsed, or not rinsed enough, some sand might have gotten into the return pipes and some could be sitting in the bottom of the pipes running back to the pool, but you'd expect that to be gone by now.
To check the laterals, you'll need to disconnect and drain the sand filter, remove the sand (save it in a wheelbarrow because you can re-use it), and then you can inspect/repair the laterals. A wet/dry shop vac can be used to suck the sand out. Our pool builder said it's not uncommon for the people in the factory not to seat the laterals fully, and we checked all of mine before adding the sand.
The reason the sand comes out after restarting the pump after vacuuming is because the flow rate is higher without the vacuum attached, so more flow and more chance to move any sand that's laying in the pipe, or more force inside the filter pushing sand through a cracked lateral or poorly connected lateral. You mentioned removing an eyeball, which would have allowed more flow as well.