The beauty of context filters is that according to Tableau's Order of Operations, they are executed before Sets.

This means that based on what Region's you've selected - Tableau will first only preserve the rows for those Regions. THEN, after this it will compute the Set , i.e , Bottom 10 products in each Region.
1) First let's create a set to compute the Bottom 10 Products by Profit.

2) Next, take region on the Rows Shelf followed by the Set we just created. Drag Region and the Set to the Filters Shelf as well.

3) Now, try to only visualize the data for the South Region:

4) The problem right now is that Tableau is computing the Set first (Bottom 10 Products), and then applying the Dimension Filter - South Region and hence these values are incorrect. Note how these aren't even 10 products, but rather just 8. To fix this, simply add Region to Context:

Upon doing this, we get the correct answer as :

Reference:
https://help.tableau.com/current/pro/desktop/en-us/filtering_context.htm