If you have are not a permanent resident, or citizen, and only have a visa will you be fined?
Nonresident aliens for tax purposes are not subject to the individual mandate. Resident aliens for tax purposes are subject to the individual mandate.
Essentially if you live in the united states and pay taxes, even if it's on a VISA, you can use the Marketplace and will need to have coverage or pay a fee.
The bottom line, it depends on your specific situation but as a rule of thumb: If you file taxes in the US, live in the US for more than a month in a year, and are lawfully present, then you need Major Medical coverage (not travelers insurance or short term health insurance).
On the plus side, many different immigration statuses qualify you to claim premium tax credits on form 8962 when you file taxes. See HealthCare.Gov below for more information.