taxonomy terms array not working

It looks like the problem is here:

'terms' =>  $term

where in your case it’s like:

'terms' =>  "array( 'peoria', 'adams' )"

but it should be like

'terms' =>  array( 'peoria', 'adams' )

By looking at your code snippet, you could try

'terms' =>  explode( ',', $term );

since explode will return the array you are looking for.

So you shouldn’t construct the array as a string.

Check for example the PHP manual on arrays here and explode here.