Logically you cannot autopostback while waiting to postback until the number of selections have completed because you don't know when the selection has finished, but there are ways.
If you abandon the idea of a server side control at all, you can do magic with JQuery and AJAX in this problem field. Server side controls are problem childs on the web, because they only exist while request is being executed on server, but they still need their state for the next request...
Most modern web approaches abandon server side controls for instance one of the major differences between web forms and mvc is that there is nolonger a 'Page' as a control container.
Therefore consider making a different implementation, not using server side control at all, like this one:
Bootstrap Multiselect | jQuery Plugins[
^]
Then you'll just handle the values in your postback (from jquery) or even better your ajax call (from jquery)
Here's an example of using page methods below, if your inital load has place necessary values to control this on the client (make sure), then jquery can interact with client and make asyncronous updates wich all in all gives a very nice look'n'feel to your site as it stops 'jumping' when users click.
Using jQuery to directly call ASP.NET AJAX page methods[
^]
So passing the name of the instance of the container name of a user control to the client side can be done for instance like this:
[
^]
and adding eventhandlers to a dom element using jquery like this:
.click() | jQuery API Documentation[
^]