Calls made or received on Burner count against your cellular phone plan voice allowance - though unlimited phone plans are common these days, so this may not be an issue. Texts sent or received count against your data only (and don’t use much data at all). + Does Burner use the texts and minutes on my phone plan? The recipient only sees your Burner fake phone number.
The texts appear to the receiver just like they would a normal text message. You create text messages from within the Burner app. This functionality acts like a barrier that prevents callers from hitting your personal number's voicemail. If you do answer, you'll hear “press 1 to accept this call.' Pressing 1 puts the call through to you. If someone calls your Burner and you don't answer, the call goes to your Burner voicemail. The recipient on the other end of a call or text will only see your Burner temporary phone number on their phone.
This is why it looks like your Burner is calling you when you receive a call and why it looks like you are calling your Burner when you dial out. We reroute calls coming to your Burner and send them to your cell phone so your personal number stays private. + How does Burner protect my personal phone number?