For L4* products, the default mode of the system is “Single-stratum” processing. That means that the entire site (one or several tiles) will be processed as one stratum -> the classifier will use all the provided in situ data to create one single classification model -> the classification model will then be applied to each tile of the site. Therefore of course you don’t need in situ data covering each of the tiles. But please, be aware that the spatial distribution and the diversity of your dataset will be a direct driver of the quality of the output maps.
In case you are providing the system with a strata shapefile (possible when editing your site in the GUI from v1.8), the system will use this shapefile to stratify your site and build one classification model for each of the strata. In this situation, each stratum have to be covered by in situ data samples. The resulted output map will be a mosaick of the individual stratum classification.
Finally, if the output was processed with multiple strata, you should get different training/valdiation polygons split in the output products allowing you to check which samples have been used for the training over each stratum.
Let me know if it helps,