I'll collate the info from the Comments above into an Answer on what's causing this and what to do moving forward.
What is causing all these cracks and is it likely to happen more?
These look like classic, textbook in fact, drying cracks. As they've occurred after the wood was supposedly dried it seems likely it was poorly done, either too quickly (leaves the interior too damp), or incompletely (moisture content was left too high throughout).
Now this is spalted wood, spalting being staining/colour changes that occur due to fungal action. And it's important to realise that the material is inherently undermined because, not to put too fine a point on it, this is fungal decay. And each black boundary line surrounds a unique area of fungal attack; while the wood can be quite sound in some places — with no apparent change in strength, only in colour — in others it can be soft and 'punky' (sponge-like and crumbly). And everything in between.
So what you get with spalted wood is always a bit of an unknown quantity. However, cracks of this number and severity should still not occur if the wood has been dried to a decent standard, as of course it should be if offered for sale by any commercial source.
The OP has indicated that returning these slabs isn't an option, but for future readers do investigate this route. Many woodworkers, and at a guess the majority of pros, would seek to return wood that behaves like this, or get a complete refund!
What to do now
Because the cracking seems like it's ongoing it would not be advisable to flatten the surfaces or fill right now, but instead leave the wood to settle down as it reaches EMC (equilibrium moisture content) with its new surroundings.
How will you know the wood has settled? You'll get no new cracks. This may sound like a wisecrack but it really isn't, the wood will eventually stop cracking. And it should be left to get there at its own pace. Patience is key with this sort of thing, it's hard but don't be tempted to try to stick to an arbitrary timescale.
Normally, to allow new wood that you've bought to reach equilibrium with the conditions in a home or workshop you need to leave it a minimum of a fortnight. But that's for wood of typical thicknesses, slabs take longer naturally (not just because of their thickness but also the width and length... that's a lot of interior wood volume).
'Punky' wood, and what to do about it if you find it
For anything that'll be used much and not just a decorative item it's important to locate and deal with any punky areas. Apart from the importance of durability in something like a dining table, this can actually be needed just to achieve a uniform finish — the soft zones can be so soft they're impossible to machine, hand plane, scrape or even to sand properly, so hardening them up is frequently necessary.
It's reasonably common to use superglue for this purpose especially in wood turning and for small projects like jewellery boxes, but CPES (clear penetrating epoxy sealer) is also used, particularly on larger stuff as you might expect.