The circuit proposed does not have properly defined threshold levels.
The transistor starts to turn on when the Base - Emitter voltage reaches about 0.5 Volt & is fully on when it reaches about 0.7 Volt.
So the delay time will depend upon the transistor's current gain (β or hFE) & Base - Emitter characteristic - both of which are temperature dependent. (Hence the delay is temperature dependent.)
Also, since the Collector current rises slowly & the Collector voltage falls slowly in proportion (according to Ohm's Law), the power dissipated in the transistor rises from zero to a maximum when the Collector voltage is at about Vcc/2 (6 Volt in the case of the circuit shown above) & then falls amost to zero when the transistor is saturated.
You therefore need to be careful that the transistor dissipation does not exceed its limit when the collector current is in the active region (ie. not in cut off or saturation). The collector current will pass through the active region when it is rising & later when it is falling (ie. when the relay is to be released).
The relay will operate when the collector current reaches the relay's operate current level & later release when the current falls to the relay's release current level.
Hystersis is provided by a positive feedback mechanism that clearly defines the threshold levels.
When the capacitor voltage rises to the upper threshold, the device output switches rapidly.
The same occurs when the capacitor is discharging but at the lower threshold voltage.
If you look at page 3 of the data sheet of the 40106 attached, you will see that, for a supply voltage of 10 Volt, the positive threshold is typically 5.9 Volt & the negative threshold is 3.9 Volt.
Therefore, the output will change rapidly when the capacitor voltage rises to 5.9 Volt and will change rapidly later when the capacitor voltage falls to 3.9 Volt.
Thus the transistor (not shown in my diagram) that switches the relay is rapidly switched on & later off so there is no danger of it being damaged by excessive power dissipation while in the active region.