Termini back to FCO airport, four hour time limit on leonardo express online ticket?

Confused? Some sites say there is a 4 hour time limit on Leonardo Express ticket from Termini back to FCO airport? But, other sites, say there is not for online ticket, but there is four paper ticket? I would prefer to buy it online the night before as when we get to termini station it will be rush hour and my daughter does not always do well with crowds/transit. Would hate to have a problem at ticket kiosk, or have to stand in a long line waiting to buy one from an attendant? Online is so much better. Flying Ryan Air, so know we need to be at airport at least two hours in advance even though it is a domestic flight, Roma to Palermo.