As Robby mentioned, there are no 100% measures how to prevent such behavior. The fleet carriers owners can change their market offer, prices or docking access any second and updates to 3rd party tools will be always behind. We can only try our best to mitigate excessively dynamic changes and provide as reliable data as possible.
How it currently works on Inara - the market data are updated via EDDN (same as EDDB, EDSM, etc.) from the various tools. On top of that, Inara is doing daily sync of fleet carriers owned by Inara users having their accounts linked (this also apply to manual import requests). With all of that, the carrier properties like docking accesses are updated from the journals and such carrier synces. And even on top of that, the carrier locations are updated by EDDN, journal imports and carrier sync. So, those are sources to get as much actual data as possible on the various fleet carrier aspects at the moment.
On the outputs on Inara - no fleet carrier prices are listed if the data are older than 8 hours (I think it's 8 hours, not sure now, but it's something like that). The prices that are older than 48 hours are completely removed. Only carriers having docking access set to "All" (are marked with blue "A" in the lists) or unknown are listed. In other words - the listed commodities shouldn't be older than a few hours and possibly are being on accessible carriers or those which may (or may not) be dockable. As mentioned, the problem is that any of the property (availability, price, access, location) may change very fast. If the limits will be set too tight, it may provide no data at all. If it will be too benevolent, it will be even greater mess.
I am aware the situation is not perfect, although Inara is trying to provide somehow reliable data. But I have a few ideas how to make it better. For a start I will start to make carrier synces more frequently (twice a day), I will probably filter out carriers with unknown states sooner and maybe I will establish some mechanics where Inara users will mark their carrier like "I am a stable market, feel free to trade here!" and if it won't prove to be right, they will get some penalty in the listings (that's just a rough working idea for now, it has some flaws). I believe such steps may make the listings more useful to everybody.