The workaround to this is to back the databases up to one tool and then to *copy* those backup files to the other tool. The best recommendation I have in these situation is always to run “regular” SQL Server Agent job backups to a file location (either a local or network drive) and then to have your third-party tool use file backup for the actual BAK/TRN files from that location *rather* than running the “database agent” on the third party tool to backup the database directly.
In this model the third party tool never directly touches SQL Server – in this client’s environment you would run SQL Server Agent jobs similar to the current maintenance plan (although something better than maintenance plans, such as Ola Hallengren’s scripts or maybe MinionBackup) to backup to actual disk (in thiscase the B: drive) and then use Arcserve to backup the files that have been written on the B: drive.
There’s good advice around not using multiple tools to take backups. This eliminates the possibility of needing to track down backups from two separate devices in order to restore to a point in time (e.g., if some of the log backups are on one device and some on the other).