Anomalous behavior of transform with Fourier()^2 space

transform and itransform behave strangely when used on a TensorSpace made of two Fourier spaces:

using ApproxFun
S = Fourier()^2
itransform(S, transform(S, [1.,2.,3.,4.]))
# gives [2.5, 3.0, 2.5, 2.0, 3.5, 4.0, 3.5, 3.0, 2.5, 3.0, 2.5, 2.0, 1.5, 2.0, 1.5, 1.0]
transform(S, itransform(S, [1.,2.,3.,4.]))
# gives [1.0, 2.0, 3.0, 4.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]

I'm expecting both lines to return [1.,2.,3.,4.], but this is not the case (this would work with S=Fourier()).
At first sight, the issue is that transform adds a bunch of zeros at the end of the output.

I don't know if the truncated output is actually correct. With truncation transform followed by itransform indeed returns the original input (and conversely) .

Start by running the Julia reproduction in the issue with S = Fourier()^2 and compare both transform/itransform round trips with the single Fourier() case. Trace the transform and itransform behavior for the tensor-product space and determine whether the added zeros are expected; done means the two round trips produce the expected values or their truncation behavior is clearly corrected and tested.