It should still work that way - though you are not the only person who has said they have problems.
When you open a model you can choose whether to open the output or the input file but once it is open you should be able to switch between the two using the blue forward and back buttons (top right/left). It should not rerun the model unless something has changed.
I have tested this with Firefox, Chrome and Safari today and it still seems to be working for me. Others who have this problem may be able to help sort out when it happens.
It is possible that you need to clear the cache to make sure the sofware is up-to-date but there are no very recent changes.
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