Press [UTILITY]
Press [F5] CONTROL
Press [SF2] MIDI
Find the parameter MIDI SYNC
Set MIDI SYNC = AUTO

This setting will allow you to have the Motif XF sequencer, arpeggiators and Tempo driven effects reference the TEMPO as received via MIDI IN, but at the same time it allows you to play (audition) what you want to do without having to have your DAW running.

We can only give you half the answer and a bit of clue as to what you need to learn to do in that DAW:
Most computer based software defaults to using the least amount of resource as possible. So you often have to activate CLOCK OUT. That is many DAWs do not automatically send CLOCK tempo out via MIDI. You have to manually make that setting.

Cubase, for example, does not. You have to go in and activate MIDI CLOCK and select which MIDI Ports it is going to be sent on. Since Studio One is very similar in design to Cubase, you probably have to find out where it sends MIDI clock and make sure you are sending it to the Motif XF on "PORT 1" if you are using USB to connect your XF ("Motif XF Main" if you are using FW).

Now when you start your DAW, your Motif XF is set to reference the tempo as set in your project. And it will dutifully follow all tempo variation, if any. You still have to trigger arms by musically playing (triggering them) in time. If you miss the downbeat, you will be punished because if you are late the entire arpeggio will be clock shifted late.

Say you are 30 clock pulses behind the beat. The entire arp phrase will consistently remain 30 clock pulses behind the beat. So make sure you play on time (as always) it is no different than manually playing, it is your responsibility to play on the beat.

You don't say (so we will not go to deeply into this) what you intend to do with the Arpeggios... If you are attempting to record the Arps as MIDI then you will need to do some additional setup... Local Control will need to be ON and the MIDI signal must be prevented from echoing back to the XF during record.
If you are recording the Arps as AUDIO, you still must have Local Control ON.

The XF's Arpeggiators are located such that you must play the keys to trigger the arpeggiator, the arpeggiator then generates the MIDI data you want to record. so an entirely different setup is required to record ARPS to external DAWs as would be used to record you manually playing the keys. In fact, when recording MIDI data generated by arpeggios, most times you do NOT want to record your trigger notes, just the notes generated by the arpeggiator.

Hope that helps.