It depends on how much fuel and supply you bought on the black market If I remember right, if you buy/sell over 100k credit's worth on the black market then it's an automatic rep hit, but even below that, as your suspicion level rises yes patrols will go after you for inspections. You can see what your suspicion level currently is when you mouseover the black market.
The 30% tariff is basically an additional cost for not getting any inspections, while buying/selling on the black market is cheaper but risks inspections.
As far as I understand it, not so much a hard cap of 100k on black market or anything, just that you need to be willing to also balance trading on open market with black market. Since rep loss isn't calculated until you leave planet, be sure to buy enough stuff on open market to drop suspicion before leaving (assuming transponder on, if transponder off, go to town). That generally prevents the auto rep loss from factions. Just a huge pain 'cuz you gotta keep mousing over markets to check suspicion levels. A more dynamic/less mousing over system would be nice.
Once you leave the market, gotta be ready to e-burn toot sweet, though. I usually run a couple of ox's when doing this, people really underestimate ox's when smuggling (oxen?). Plus, Mules with shield cargo holds also help, but sorta stupid since all the cargo calcs are hidden. Just have to assume that some amount of cargo is considered "hidden" compared to total cargo space, and I guess game attempts to assign all illegal cargo to such "hidden" areas automatically. Dunno if there is really more complicated code than that, though.
As a side note, why can't shielded cargo holds be found as a schematic? Not disputing ripe for exploitation (probable reason), just seems like that is just not even an option to find a schematic for. Mules and Oxen FTW?