It’s not typical for designers (especially Print designers) to use ’ems’ or ‘percentages’ in Photoshop. In fact, the ’ems’ unit of measurement doesn’t exist there. ‘Percent’ does so that might work.
A good web designer should provide measurements to all of the elements of the finalized design. Of course, the unit of measurement will depend on what you will both agree on. Nowadays, I try not to worry too about pixel-precision because of the ‘Responsive Web Design’ movement.
Rather than treating yourself for a surprise, you should discuss with your designer what type of deliverables you’re expecting from them.
Educating the designer on what can and can’t be done on HTML and CSS would be very good. It could save you or your designer some time from doing some unnecessary work. Of course, ‘Educating’ is a slightly heavy term and it might be something that you won’t be able to do in one sitting but it’ll definitely help you in the long-run.
A good designer will do his homework and just tell him that Web design is way more forgiving than Print design and he’ll get the idea ;)