You need to connect the heater voltage to 4 only. Connect the heater from 5 to the other side of the supply.
These are the parts of the data sheet that are related to your question.
“If the load circuit is a heating control system, be sure to connect the load to terminals 4 and 5. If the load circuit is a cooling control system, be sure to connect the load to terminals 4 and 6.”
“We recommend using an external relay to extend the electrical life of internal relays when driving a large capacity load. This is particularly important when the output relay is switched frequently (e.g., with proportional control).”
“Control output Relay output: SPDT, 3 A at 250 VAC, resistive load (switching capacity: 330 VA)”
The data sheet is not very well written. Terminal 4 is the common point of the internal single pole double throw (SPDT) relay. Terminal 5 is the normally-open contact and terminal 5 is the normally-closed contact.
If the heater requires no more than 3 amps at 250 volts AC, you can connect one side of the power supply to terminal 4 and connect the heater between terminal 5 and the other side of the power supply. If one side of the power supply is a grounded neutral, connect that side to the heater and the hot side to terminal 4.
If the heater needs more than 3 amps at 250 volts AC, you must connect the coil of a higher current and/or voltage rated relay to the controller instead of the heater. Connect a contact from that relay between one side of the power supply and the heater. Even if the heater needs less than 3 amps at 250 volts AC it would be better to use an external relay. “This is particularly important when the output relay is switched frequently (e.g., with proportional control).”
PS
2.25 W is a very small heater. Are you sure it is not 22.5 watts, 225 watts or 2.25 kW?
PS2
I think this confirms that the controller power supply is not internally connected to supply the load:
"If a single power supply is used for the E5C2 and the load, the supply voltage of the power supply may vary greatly when the load is open or closed if the capacity of the power supply is not large enough. Make sure that the capacity of the power supply is large enough so that the supply voltage range will be always from 90% to 110% of the rated supply voltage."