I want to let you know how filtering on something like a tag works in Photo Mechanic and why it would be slow on a large number of images. The tag is part of each image's metadata that needs to be read from the file and performing this reading takes time. PM can get the data it needs from the files on a fast local drive on the order of a hundred images per second. If it is on a network drive, it can drop as low as tens per second. PM generally is set to not filter on anything at all and as such it can get directly on to the business of showing you your images. But in order to filter and only show the tagged images, PM must get the metadata for all of the images before it can filter out the non-tagged images. If PM has already read the metadata on all of the images, then the filter will happen in mere seconds. But if it hasn't read all of the metadata yet, then it must read it all and depending on how fast PM can access that data, the filter can take a long time. In your case this filtering is taking minutes.
So with 15,000 images, even at 100 images read per second, it will take 150 seconds (2.5 minutes) to begin the filtering process. If PM is only able to read the metadata on 10 images per second then it would take 25 minutes to begin the filtering process.
PM does read all of the metadata in the background while you browse your images, but if it hasn't read it all then it can take a long time to do any kind of filtering. The Sort Cache which was introduced in PM 5 does help with this task, but the Sort Cache is of no use if the metadata hasn't been read fully at least once prior to the sorting/filtering. If images have changed since the sort data was cached, then it must be re-read to make certain that the sort data isn't stale. If your images don't change often, then the Sort Cache can be quite beneficial.
-Kirk