I am assuming from your description that 'sticky' headings in this sense is analogous to 'frozen' headings - I'm not sure how this could work otherwise (i.e. if the headings are 'pinned' to the top of a web page - given that you are going to have multiple tables - having multiple table headings pinned in place could get messy).
So to answer your question whether or not sticky table headers should be used for multiple tables on the same web page - it's best to avoid that approach.
If you want a good example of how you could do this, have a look at TSN's NHL Standings Tables.
In this example, you have frozen headers, frozen columns, tabs to switch between tables, multiple stacked tables - and it's RWD (Responsive Web Design - the UI, using one design, will adapt neatly to phones, tablets and larger screens).
Also note the 'left-right' scrolling of the table is done by either tapping or clicking on the side of the table you want to scroll to.
All-in-all, this is the best example of UI/UX I've seen that's RWD and can handle multiple tables on the same web page, with frozen headers and columns, and will give you great flexibility.
Hope that helps!