I'm amazed and horrified by the idea of applying for only two postdoc positions in mathematics, one for a year and one for six months. You should talk with your advisor and other senior mentors about this as soon as possible. Maybe your personal situation is radically different from what I imagine (for example, I have no idea what country you are in), but it sounds like you are doing something extraordinarily risky.
For pure mathematics in the U.S., it's common to apply for fifty to a hundred postdoctoral positions. Applying for ten is a mark of great confidence (or foolhardiness), and applying for two is almost unheard of. Nobody would be surprised or upset to learn that you had applied for other jobs. Instead, they would be unhappy to learn that you hadn't. That would make them wonder whether they had somehow miscommunicated the odds of being hired, and whether they were about to play an unwilling role in damaging your career.
The applications will be decided by a committee, not the professors concerned.
This is a key factor. It's hard to imagine that you are the only one to apply, or the only one to receive positive feedback from a potential mentor. In fact, you might not even be the only one to receive positive feedback from this specific mentor. (It's common to tell several people that you'd be happy to work with them if they are selected by the committee, even if the committee will choose at most one.) In other words, by default you should assume you won't get either of these jobs. Maybe you'll be lucky or you have an exceptionally strong application, but it's safest not to count on this in your plans.
I should note that I'm a little puzzled by two aspects of your question. Applying at the end of March would be absurdly late in the U.S. system, and a six-month postdoc would hardly be desirable at all except in conjunction with another job (or if you graduate in December). This suggests that you may be working in a very different system from the one I'm familiar with, in which case you should seek local advice or be very explicit about your circumstances.