Can anyone help me with data from sequencing center

Yes, as I already wrote and as it is written in the q2-cutadapt description it will remove the primers (provided) and any preceding sequenses (including barcodes in that case).

That's right - this time you should use trim-paired script since the purpose is to delete primers from already demultiplexed reads.

That's an example from my pipeline

qiime cutadapt trim-paired \
    --i-demultiplexed-sequences demux.qza \
    --o-trimmed-sequences trimmed.qza \
    --p-cores 6 \
    --p-front-f CAAGRGTTHGATYMTGGCTCAG \
    --p-front-r TGCTGCCTCCCGTAGGAGT \
    --p-match-adapter-wildcards \
    --p-discard-untrimmed \
    --p-match-read-wildcards

All primers are provided in the 5'-3' orientation.

PS. Since this thread is becoming too long and the point of discussion already diverging from the original question, please create new topic for new questions (after performing quick search on the forum to make sure that this question is not already answered). This approach may help other users who'll encounter the same issues in future).

Best,