While on this topic, company got back to me and showed measurements that don't show the resonance in the woofer that I measured:
So maybe that is an issue with the sample I received.
One should always be somewhat cautious when interpreting near field measurements.
As a very rough approximation one can say that up to 200-400Hz (depending on the LS dimensions, mic distance from woofer dust cap,...) the agreement of near field measurement (BR port + woofer) and NFS on-axis measurement should still be quite good.
Then baffle step and edge diffraction have more and more influence on the frequency response of the loudspeaker - which the near field measurement does not capture. In addition, possible Eigenmodes/resonances of the cone, surround and dust cap of the woofer, can have a stronger or weaker effect in the near field measurement than in the anechoic measurement of the NFS.
Above 1000Hz one should be very careful with the interpretation. If the NFS measurement (e.g. CSD) shows no abnormalities, one should ignore the frequency response of the woofer near field measurement above 1kHz.
For example here is a comparison of a near field measurement (red plot) of a 8'' woofer with the "quasi anechoic" (gated, ignore FR below 200Hz) measurement (blue plot) of the speaker woofer.
You can see the influence of the baffle step above about 300Hz. Above roughly 1 kHz there are resonances in the near field measurement that have hardly any influence in the far field measurement (e.g. see 1), others occur in both measurements (e.g. see 2) and there are resonances that do not occur at all in the near field measurement (e.g. see 3).
The resonance around 5 kHz in the CSS Criton 1TD-X woofer near-field measurement can therefore be a measurement artifact, a disproportionately severe reproduction of an existing resonance or a driver manufacturing error.
The manufacturer's measurement, seems to be the measurement of the woofer in infinite baffle, but not a near field measurement of the built-in driver in the cabinet. If you look closely, however, the break-up resonances in this measurement also starts in the 4-6 kHz range.
The CSD of the CSS Criton 1TD-X also shows a slight resonance around 5kHz. Unfortunately, the scaling is only 20dB instead of the usual 30dB, but you can still just see the 5kHz resonance and it is attenuated by about -15dB (if we exclude the tweeter as the cause)
For example, it could be a dust cap resonance that appears more powerful than it is in the near-field measurement due to the missing baffle step.
The manufacturer could simply perform a near-field measurement on another finished CSS Criton 1TD-X speaker, then we would have a comparison.
If the 5kHz resonance is not due to damage to the woofer, one would have to take a closer look at the decay behavior of the resonance - but even now, the 5kHz doesn't seem to be too much of a problem (CSD with 30dB scaling would provide information about this).