From the ‘757 Captain III’ Manual Part II – Aircraft Systems (CS757CAPTAINIII_MANUAL_PART2.pdf), page 86:

3. Flight Level Change (FL CH) Switch
Push -

   - selects FLCH mode and sets IAS/MACH window and command airspeed
     bugs to current airspeed

   - FLCH displays on each FMA

   - AFDS pitch holds existing airspeed and A/T sets required thrust, limited by
     the thrust limit for climb and idle for descent. When selected altitude is
     reached, pitch mode changes to ALT HOLD and A/T changes to SPD
     mode

   - with FLCH mode displayed, pushing switch resets IAS/MACH window and
     commands airspeed bugs to current airspeed

   - changes thrust reference from TO to CLB if above 400 feet radio altitude.

So going by the underlined information above, if the 757 is doing 213KIAS when you press the FLCH button, then YES, that is what it should do. For it to climb at 250KIAS, you need to wait for the 757 to reach that speed before pressing the FLCH button.