Do you wan´t to use google´s updatable webview on a cm rom?
well too bad, even if you install and disable the built in webview, the system still dosen´t uses it, so what can we do?
modify a config in the framework called
"config_webViewPackageName" from com.android.webview to com.google.android.webview
you can do this via xposed with http://repo.xposed.info/module/net.typeblog.webview
however xposed for 5.1 is glitchy and will break a lot of optimizations if you are running a based cm run that has those.
so the solution? well flash the zip below, its a modified framework from cm12-13/04/2015 (DD/MM/YY btw)
Download zip from the link provided
Flash via recovery