There were three (3) general application "models" for zimmerit - and these offer you some choices as to what pattern and what is revealed when chipping zimm...:
First came field-zimming, where rear-area shops and vehicle crew applied stuff shipped to the front units. This started up in early 1943 when zimm was first issued and probably pretty much ended by SEP or OCT 1943. This stuff would axiomatically have gone on over the tank's final coat, and "patterns" were whatever the guys decided to do at the time. This "field zimm" could quite possibly reveal a dunkelgrau or dunkelgelb finish coat, or even a camo pattern (think about the cool possibilities!
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when chipped off. Probably NOT a primer coat, as that would entail lifting all the final / camo paint and leaving the primer... seldom the case, I'll bet. Of course a chip could remove all the paint and reveal bare metal and surface-rusting. Choices!
Next came application of zimm onto vehicles at the rebuild / refurbishment factory (mostly Nibelungenwerk) - from late SEP 1943; panzers sent back for rebuilding (including Ferdinands and "Brummbar" surviving Kursk in summer, 1943) were zimmed before being re-issued, if they didn't arrive with zimm. This zimm went on over whatever colors the tank wore... rebuilds were unlikely to have been stripped of paint and re-primed - but newly-added metal would have the primer option... Patterns were "standardized". Nibelungen may have continued this "semi-factory zimming" to late 1944, as there was a continued-but-dwindling "supply" of pre-SEP 1943 zimm-free tanks in for rebuild. As zimm application ended by order in SEP 1944, I would be pretty sure that the refurbers stopped their application at that time. Again, a "refurb" tank with zimm could chip to reveal prior paint, or primer on putative new parts, or bare or rusted metal. Choices!
The last zimm "model" is the factory-application of standard patterns during tank assembly, from SEP 1943 thru to SEP 1944. This last approach was both the most standardized and the most likely to have a primer base with the 2-layer application process, followed by vehicle base-coats and, in some cases, factory camo jobs.
So... you have some choices indeed! NO tanks assembled before JUN 1943 came with factory zimm - IF you model such "older" panzers, they would either be field-zimm or a rebuilt vehicle. Both chip to reveal base-coats and maybe camo. SEP 1943 - SEP 1944 factory-zimm are standard patterns and could have been applied onto primer.
Hope this helps!
Bob