Those experts have themselves publicly aknowledged that they were invited to the country and all of their expenses including travelling and work fees were paid by the party, which loses the most by having e-voting, Estonia's Central Party. Two books on the subject have also been funded by that party and other experts have said, that the systems are more secure than the ones that even banks use.
About the Central Party(Keskerakond). They have a very specific voter, namely very old people and Russians who do not want to fully integrate into Europe. Most who vote digitally are younger people who do not support that party. E-voting has also very strongly increased the percentage of people going voting, those are working people and youth, a demographic that is totally against the Central party's agenda.
The Central Party is despised for a number of reasons: Sell outs to Putin(Recently the head of the party made a statement in Russia saying the the Ukrainian government in Kiev is illegitimate), stupid things like municipal police which are used to tear down rivalry campaigns and annoy the general public and this unit is totally under the control of that party, a municipal store, TallinnTV which pretty much nobody watches and the people doing it are saying that it is awful(used for party propaganda and funded by the city), a municipal bank which will not even be capable of half the services our local banks or the Nordic banks can provide. The party is also working to stop the integration of immigrants into our society and it has worrying ties to Moscow.
The party controls the city of Tallinn and is making it into a pseudo-welfare city that can't hold itself up. The only reason that party has so much power is because of a lot of very old people voting for it and unintegrated Russians. Actually the only regions it wins in is Ida-Virumaa(pretty much Russian) and Tallinn.
Really, the amount of what the party is doing wrong and how bad the head of the party, Edgar Savisaar, is to Estonia is probably worth an entire book. Unfortunately I believe that international press on them is lacking.
PS: They also want to abolish a day in the city which is dedicated in memory to everybody who was influenced by the Soviet deportation, which they got a lot of criticism for and is another grab to gain popularity in the Russian spheres.