It is very possible for pressure in a tank to cause uplift. Anchorage critera are specified in API 650 Table 5-21. If your code of construction is different and you care to disclose what it is, I may be able to find the appropriate reference.

What I have come up to is that the dirty media causes pressurization of the "small tank" and since the bottom plate is only 1/4" it is causing the bottom plate to bow and thus lifting the entire shell up. Once the bowing happens it also causes the inlet pipe to deflect and causes more uplift as well. Now, one more question I am unsure of is when the "small tank" starts to pressurize the HGL starts to increase as well. Does this event cause boyance forces on the top plate (I consider it a plate now because the filter is dirty and not much water is flowing through it)and causing a moment about the centroid?

I have one question about the situation, is the media capable to generate pressure in the liquid beneath of it? Normally lifting of tank is observed when there is increase of pressure of inside liquid/vapor. For example: the over pressure during a) hydro/pnumatic test b) failure of pressure relief valve at operation stage. Looking to the described situation it seems that the shell(with bottom) portion near liquid zone has lifted more but toward baffle side(empty zone) not much. Please confirm this. I also advise to check that there shall be sufficient mass of the concrete such that upward force on anchor bolts will be balanced. Otherwise anchor bolts will not fail due to pulling force but the concrete portion itself will be lifted from the surrounding soil. I am also worry that there shall be sufficient thickness of baffle plate, otherwise it will bend due to differential pressure induced due to liquid level difference plus the effective pressure due to mass of the media on liquid.