Hi guys,

apologies if this question has been asked before, I知 new to this forum, please feel free to redirect me. I have a 2010 Honda Civic 1.8LXI Automatic.
Here is the issue I知 facing:
1. When the car is cold, I feel a very strong vibration in the entire car, almost feels like a massage chair.
2. When I知 driving, while the temperature is still low, the vibration persists particularly at low RPM (around 1000 - 1500 RPM).
3. While driving, at low RPMs at cold temperatures, if I release the accelerator, I hear a strong momentary whizzing sound, complementing the vibrations
4. Once I知 driving faster and the RPMs are higher, either I don稚 notice the vibrations or the vibrations are minimal to none.
5. After the car warms up, the vibrations are minimal or negligible
Some points to note:
1. I had a service done (oil change, spark plugs) about a month ago
2. I showed the car to the same mechanic who services the car - he claims the Engine Mounting RHS and LHS need replacing - the total cost of which is ZAR9,200 (about $650)

please advise if the mechanic痴 diagnosis sounds fair enough? The fact that the vibrations change with RPM and temperature makes me think, it痴 not a mechanical fault? (but then again, My knowledge in cars is close to 0). Any suggestions? Anything a noob could try to fix it?
thanks in advance