"my First name only into the Given Name(s) field"
If it asked for "first name" a single name might be acceptable. But it didn't.
Notice the "(s)". That means that there can be more than one name.
Notice the "Given", that means all but your family name, which was inherited not given.
The form didn't ask for "First name"; it asked for "Given name(s)".
Many countries are improving their forms by saying "Given" rather than "First", since there are many societies where the first name is actually the family name.
(e.g. in Chinese, "Xi Jinping", "Xi Jin Ping", and "Xi Jin-Ping" are all valid Romanizations of "习近平". "Xi" is first, but it is the family name.)
EDIT: @Voo says that the form contains this instruction:
Please enter exactly as shown on your passport or travel document.
That should remove any confusion. Whatever names are on the passport you are going to be using should be the names you use on the form. No more, no less.