Hi Flutterby,
Welcome to the cafe :)
Some practitioners are just not so good at keeping their own 'stuff' to themselves when treating others and this may have been why you experienced what you did with the first person and not the second. I agree with Prosperity in that if you are feeling uncomfortable it is better to end the session; you can always use the excuse that you are feeling unwell to save any awkward discussions about not feeling comfortable with a particular practitioner. As for the exhaustion, you can feel tired, relaxed or alternatively you can feel energised by a Reiki treatment. If you were feeling totally drained then I would say that you should use some grounding and protection techniques next time you attend a meditation group.
I once had a similar situation at a Reiki share as a newbie when one of the practitioners there thought it was a great idea to press very hard on my brow chakra(third eye). I had a splitting headache and felt nauseous for hours after. It made me very aware of how not to do Reiki on others. I always put myself and the recipient in a bubble of white light when giving or receiving a treatment.
I hope this experience hasn't put you off trying Reiki again :)
Gentle Blessings
Helen