How to override page.tpl.php with view's template file
First you define a specific display in your template: views-view-field--employee--page--field-first_image.tpl.php.

Then you don't specify a display in your insert tag, making it fallback to default.

To fix your problem you need to either strip the display part of your template name or specify a display in your tag, like [view:employee=page].

I would probably go for the first solution, so your theming targets all possible displays of that view, but how you do it really depends on your implementation.