I believe this is an effect of how initial conditions are evaluated for conforming element types. Since there are nodes on the shared interface between the subdomains they will get averaged values.

If you have a known analytical expression for the decay you can define this as a "Constant" in "Subdomain mode" with for example "Expression" values "0 2*sin(pi*t)", so that the expression has value 0 in subdomain 1 and 1*sin(pi*t) in subdomain 2. Alternatively, this can also be defined with logical switch expressions as something like "2*sin(pi*t)(x>2)*(x<8)*(y>1)...".

If you absolutely need to use a dependent variable for this you would need to use the "

sf_disc0" piecewise constant shape functions as they are not connected through the edges or vertices. Unfortunately they are not selectable in the GUI by default so you would likely have to save and run the model as a m-file to use them.