DIFF and TLog backups are always related to the latest FULL backup and they don't care which job has taken the latest FULL backup.
So according to your explanations, your daily DIFFs and TLogs (Cloud MP) are based on your latest daily FULL backup (local MP). => mixture of job results
and I don't think that's something you wanted to achieve...
My recommendation would be - with a target of having the possibility to restore point-in-time - to use the Cloud MP for your regular backups and change the local one to a "Copy Only" FULL backup.