Yes, the refresher flying must be completed during the second year of Rating validity. There is no restriction on the number of flight or instructors conducting this refresher flying for any one pilot, provided that the total of 1 hr has been gained. The old CAA rule of 'no more than 3 flights and all with the same Instructor' was deleted a while ago now.
FCL.945 Obligations for Instructors
Upon completion of the training flight for the revalidation of an SEP or TMG class rating in accordance with FCL.740.A (b)(1) and only in the event of fulfilment of all the other revalidation criteria required by FCL.740.A (b)(1) the instructor shall endorse the applicant's licence with the new expiry date of the rating or certificate, if specifically authorised for that purpose by the competent authority responsible for the applicant's licence.
The idea behind this was to make it easier for a pilot, who had already gained the flying experience necessary for revalidation, to obtain the revalidation signature immediately after completing refresher flying, so that he/she wouldn't then need to find an Examiner - the FCL.945 Instructor signs the Certificate of Revalidation.
However, if the pilot hasn't
completed the experience requirements before the refresher flying, then he/she will subsequently need to ask an Examiner to sign the Certificate of Revalidation once all requirements have been met. An FCL.945 Instructor may not do so in such circumstances.