This is a common myth that opponents of Proportional Representation have been spreading around, to generate fear of change. :(
This 2-ballot system might feel unfamiliar to islanders, but it's not so scary - it's long been used in countries that have MMP - like Scotland, Wales, New Zealand and Germany.
In MMP, a party puts forward a set of candidates in every district, just like they do now, and voters place their 1st vote next to an individual candidate's name in their district.
In addition, a party will put forward a set of up to 9 'province wide' candidates. Voters place their vote for a single province-wide candidate, from the party that they would most prefer to govern the province.
The most popular candidates will be chosen for each of the 18 local districts, and in addition, for the 9 'proportional' seats, each party's most popular representatives - as decided by the voters - will be chosen to fill the seats in the legislature that party has earned.
In PEI's 2005 plebiscite a "closed list" proportional model was used, which has some degree of party control. That was not the case in 2016's plebiscite, nor is it being considered anywhere in Canada in 2019. The influence of parties is limited only to the candidate nominations: voters choose which candidates win the seats.