A fantasy story is an imaginative story that includes supernatural events , mythological creatures , magic , etc. It occurs as a strange story if compared to the normal world i.e there are not such things in normal life or what we know of , for an example we know that witches and wizards don't exist in real world but we (here I am assuming all) love reading harry potter. The Harry Potter series is a work of fantasy.
Now about fiction , so fiction is nothing but a work created from imagination but it may or may not be based on a true story , here am not saying that it is a real story but just can be based on such, fictional stories aren't like the non-fictional stories which are based on actual events and people. Fiction covers all the stories that comes from imagination.
So now how is fiction different from fantasy? As I said above all the imaginary works come under fiction. So Fantasy is a sub-genre of Fiction.
As I have read your story , it's genre comes under science fiction coz of the time travel through the portals. Sci-fi is also a sub-genre of fiction.
Now if I remember correct , the question
went by asking the answerer to write a
'Fictional' story , which you did. From
your question I infer that The person who
read your story said it was not factual (to
that person) that is why it's a fictional
story. Fictional stories don't need facts it's
a work of imagination that is what makes
it a "Fiction".