If you want to be sure talk to your roofer or the manufacturer of the roofing panels.
Rigid foam under metal roof on purlins.
Commonly these use metal deck panels over the roof structure thus supporting the insulation and a vapor retardant material on top of the deck.
Cut each sheet to the desired size using a utility knife then fasten it in place using staples or adhesive.
The best material for use with metal roof insulation is in the form of foam batting.
It will help you to eliminate problems that may come when the house becomes extremely cold in the winter and terribly hot in the summer.
However code requires them to be covered with a fire barrier on the inhabited side.
Insulating with spray foam insulation.
As far as i know standing seam metal roofing can t be installed on rigid foam.
This foam can be used on either the outside or the inside of the sheathing.
Further insulation may be added by the use of high r foam boards placed beneath the purlins.
Polyurethane spray foam metal roof insulation in order to add moisture barrier under metal roof you can spray the undersides of the roof by using a thick layer of polyurethane spray foam.
In this insulation approach rigid foam insulation board is used to achieve the sought after energy performance.
Avoids nails or screws which could penetrate the metal roof and cause leaks.
Rigid board composite systems.
It is possible to insulate from below as you suggest with rigid polystyrene insulation.
I would seal the eps against the purlins with a high grade permanently flexible caulk or spray foam insulation.
The solution i have in mind is to cut 2 foot wide strips of 1 2 thick foil poly faced eps to fit between the purlins 1 2 below the metal roofing.
There are two ways to do this put in firring nailing though nails are not used any more for this strips or purlins in steel frame construction on the roof to support it or place the metal roofing directly on a flat surface like foam insulation board or the roof sheathing with roof water barrier in the correct position in the layer.
It has to be installed on plywood osb or possibly purlins.
This will provide an air space above the foam insulation to improve ventilation on the underside of the metal roofing.
The rigid board material costs roughly 23 cents per square foot.
First nail 1x2s to the rafter sides up against the roof strapping.