It is possible that there is some sort of trouble with the ECU however it may not necessary be due to it being an aftermarket Acura ECU. It may just not be the correct ECU for your specific Acura Integra. The Acura Engine Control Unit is a very specific component, which is usually requires matching the serial number of the ECU with the VIN number of the vehicle. In other words you might not always get favorable results by simply swapping same model and make year of another ECU.
If after verification you find that the ECU is in fact intended for use in your 2000 Acura Integra, we recommend ensuring the ECU is mounted properly and all it's connectors/links are plugged and secure. You might want to also ensure all fuses belonging to the ECU are good.