A 20 ton 'Mech with a 120 rated engine (Stinger, Wasp) that does not choose to mount additional heatsinks begins with the base 10 heatsinks has enough room in the engine (taking up no space) for four of them (engine rating 120/25 = 4.8, rounded down to 4). The other six cost no extra tonnage, but must be allocated space outside of the engine.
A 100 ton 'Mech with a 300 rated engine (Atlas, King Crab) that chooses to mount additional heatsinks over the base 10 heatsinks spends one ton per additional heatsink. With such an engine, the 'Mech is able to hide 12 heatsinks away in the engine (engine rating 300/25 = 12). Despite paying the two tons to get to 12, no additional space is consumed by the heatsinks. Mounting more than 12 heatsinks costs both tonnage and space.
A 55 ton Omnimech with a 330 rated engine (Stormcrow/Ryoken, Men Shen) that only chooses to mount the base 10 heatsinks on the base chassis spends no additional tonnage, and is able to conceal all 10 heatsinks (engine rating 330/25 = 13.2, rounded down to 13) with room for a few heatsinks to spare. However, because the base chassis is fixed, adding any heatinks to that total in any configuration that doesn't change the base chassis (at which point it's no longer an Omni), any additional heatsinks added after that cost both tonnage and space. Any heatsinks above those mounted on the base chassis cost tonnage and space regardless of whether the engine could conceal them if they were present on the base chassis. If, before fixing the base chassis, the 'Mech had mounted all 13 "free" heatinks (which would still cost 3 additional tons), then they would take up no space. However, the base chassis did not, and the extra heatsinks take up space.
For an Omnimech, it's a juggling act between whether to save crits or maximize payload space.
I hope that clears up any ambiguity on the subject.