If the beam is horizontal, as in setting on horses, and the plate is vertical to the floor, you are correct. You will be welding in the overhead, vertical, and horizontal. There would be no flat position involved unless there was a groove weld, but you already stated all the welds are fillets.
The I-beam or wide flange beam is considered a rolled shape and it would not be considered to be a tubular. Tubulars are hollow sections such as a column made from pipe or a rectangular or square hollow tube section.
You would need a WPS that lists it is applicable to all positions. It is possible to have a prequalified WPS for welding fillets or grooves in all positions.
The welder can be qualified for all position fillet welding by passing fillet break tests in the vertical and overhead positions if this is a D1.1 structural application. Alternate tests would include grooved plate tests in the vertical (3G) and overhead positions (4G) or pipe tests in the vertical (2G) and horizontal (5G) positions or a single test on pipe in the inclined position (6G). I would have to believe the fillet tests would involve the least amount of time and with least cost when compared to the various grooved plate tests I've listed.
Best regards - Al