Do you mean to say that your old Mac was dual booting? I've never tried to use Migration Assistant in that scenario.
Or do you mean it contains one bootable OS and another data only partition? Migration Assistant will focus on the bootable volume. Data from the data volume/partition may be listed as "Other", but I'm not sure since I never tried using Migration Assistant in that scenario either.
Keep in mind starting with macOS 10.15+, all macOS boot drives contain multiple APFS volumes.....with one being a read-only system volume and the other one a read+write volume containing your home user folder(s) that contain all your data. This is completely normal so there is no issue with Migration Assistant.
How are you accessing the old Mac? Did you launch Migration Assistant on the old Mac as well? If so, then I would imagine it is only showing the items available on the macOS boot volume/partition and will ignore any other partition/volumes. However, I never tried it with this method when the old Mac has multiple volumes/partitions.
If the other partition/volume is a data only volume you created, then you should know what is on it. Same if it is a second bootable OS partition/volume.
You can always put your old Mac into Target Disk Mode and connect it using a Thunderbolt cable to access data on any partitions/volumes on the old Mac.
Or better yet, restore from a Time Machine backup, then you will know you are restoring the data you want.
Maybe another more knowledgeable contributor will chime in here, but your post obviously doesn't contain enough details about the setup of your old Mac as I've pointed out with the various possibilities. Knowing the setup of your old Mac will allow another more knowledgeable contributor to provide a more direct & accurate response.
