Does lawmaker's immunity cover flagrante delicto?

Section 11 of Article VI of the 1987 Constitution provides, "A Senator or Member of the House of Representatives shall, in all offenses punishable by not more than six years imprisonment, be privileged from arrest while the Congress is in session. No Member shall be questioned nor be held liable in any other place for any speech or debate in the Congress or in any committee thereof."This provision of the Great Document embodies the rule of parliamentary immunity. It has two parts: (1) privilege from arrest, and; (2) immunity in speech or debate.

Many a piece of jurisprudence has discussed immunity in speech or debate among senators and house members and its rules and interpretation are very much settled. However, recently, regarding privilege from arrest, "House Majority Leader Rodolfo Fariñas asked traffic enforcement agencies on Monday, September 18, to excuse lawmakers when they commit minor traffic violations on their way to work. Citing parliamentary immunity, he asked the officials of the Department of Transportation (DOTR) and the Metropolitan Manila Development Authority (MMDA) to give leeway to representatives who commit minor traffic violations on their way to Batasang Pambansa in Quezon City to attend a session." (https://www.rappler.com/nation/182558-immune-congress-minor-traffic-violations-farinas)

It is Project Jurisprudence's view that the constitutional privilege from arrest applies only to arrests with warrant and does not apply to in flagrante delicto arrests. The Rules of Court defines in flagrante delicto arrest, thus: "Arrest without warrant; when lawful. - A peace officer or a private person may, without a warrant, arrest a person: (a) When, in his presence, the person to be arrested has committed, is actually committing, or is attempting to commit an offense xxx." (Section 5(a), Rule 113) A different rule would open the floodgates of hell to more abuse.