The reason your 2001 Dodge Neon may have passed previous smog checks is probably due to the fact smog check regulations loosely ensured that an installed catalytic converter was designed specifically for use in the vehicle being inspected.
Smog technicians were simply instructed to visually ensure the catalytic converter was present and that appeared to belong to the vehicle; fit looked right, weld was clean, number of CATs present was correct.
Today however, the new STAR smog check program (since January 2014) has changed things. A smog station/smog technician can now lose his/her STAR status if smog inspections are not carried out to a T and catalytic converters are not visually inspected for proper model number (CARB number for aftermarket CAT) and fit.
The smog check technician must check your Dodge Neon's catalytic converter EO (executive order) number. The EO number (also know as CARB number or Executive Order) is assigned by the California Air Resources Board to California compliant aftermarket emission components. If EO numbers are not found on any CAT being inspected, or EO number found but not matching the numbers required for the vehicle the CAT is installed on the vehicle will fail the smog check for an "emissions tamper".
There are situations where the smog technician is able to locate the catalytic converter EO number but the EO number does not match up with the required CAT EO number assigned for the vehicle being inspected. In these situation it is possible the aftermarket catalytic converter was purchased and installed prior to 2009.
Under the new smog inspection rules a pre-OBD II (pre-2009) converter can pass the smog check as long as it was installed before 1/1/09 and you can provide the smog station proof of the installation date. The CAT must have been designed for use on the vehicle being inspected back in 2009. If however the installed CAT was not manufactured or approved for installation on the specific vehicle, it will fail the smog check regardless. The following is a PDF by C.A.R.B. explaining the new California CAT law.
http://www.smogtips.com/Aftermarket_CAT_ARB.pdf