Any employee, who was a state member in employment in a function at the time of the assumption of the function by a city and county and became a local member on the date of the assumption and in employment of the city and county in that function under the contract with the city and county, shall continue in membership thereafter so long as he or she continues, without a break exceeding 30 days, in that employment or any other employment, falling in the same membership category under this system, of the city and county or any other public entity in which he or she would be a member of the retirement system of the city and county except for this section. Those employees shall be excluded from membership in the city and county retirement system in that employment. A member electing membership in this system shall make the contributions to this system that would have been required had he or she been a member while in that employment.