Crontrigger plugin to be disabled when cronjobs are used?

I've configured the cronjobs in the server's crontab as described in the install instructions. Logrotate and garbagecollector are set to weekly. I also have the crontrigger plugin enabled.

The weekly cronjobs were done as expected at the beginning. They were executed once a week and I had 1 new table in the database after the log was rotated.

When my site was moved from shared server to VPS it started to become strange. The weekly cronjobs were no longer executed only once a week but twice a week. Additionally, I no longer had only 1 new table but several new tables each time after executing the jobs at one of these weekly times (record was 13 new tables). At the other of these two weekly times it still was only 1 new table in the database.

Last week my VPS had to be moved on another VPS node. And now the weekly jobs were executed 3 times a week!

I'm wondering if this is caused by having the crontrigger plugin enabled in parallel to the cronjobs in crontab. I haven't found any advice to disable the crontrigger plugin if using regular cronjobs. Should the crontrigger plugin disabled in this case? I would also like to know why several new tables are created by logrote sometimes. Is this normal or not?