Radu Tut wrote the post Managed Metadata Navigation for Multiple Site Collections in SharePoint 2013, stating: "When you try to bind the same navigation term set to a new site, you will get a message that says the term set is already bound to a different site, and if you choose to proceed, the navigation settings for the other site will be broken."
I don't know if you got the error message in the first place, but there are ways to overcome this issue in two different ways, according to Mr Tut:
Create a new term set, and pin it to the source term set. The new term set is a copy of the source term set, and it can be used in a new site collection. ... However, if you have a lot of site collections, this can lead to a very large number of term groups and term sets in the term store.
Depending on many site collections you will use, one option is better than the other. If you only have two site collections (however unlikely this may seem) I'd make a copy of the first term set. Slick, easy and fast but it will cost you later on in maintainability. Updating two (or more) different term sets for global navigation is never a good idea. Ask your customers how they want this executed, using the following slide:
Still, using the second technique is expensive and custom made. When you have this working on twenty site collections this is great! The choice is yours! Do you want to develop a solution as in "Building global navigation in SharePoint 2013" or do you want to copy terms?