What are your water parameters - ammonia, nitrite, nitrate, pH, temp, KH, TDS?
If they ate in the first 1-2 days, it's a great sign that they weren't shocked by the move and acclimated quickly to your water and tank. At 1st approx. this could rule out that something could have gone wrong during the transport and acclimation, e.g. gill burn by ammonia or by a pH jump, water being vastly different, etc.
Getting sick on the 3rd day may indeed point out to a disease they contracted in the new tank. What kind of a disease - parasitic, bacterial, viral can be very hard to say. A sequence of wide spectrum treatments might eventually help.