Do you first feel the touch (pleasant, unpleasant or indifferent) or do you first identify it? Or is it all at the same time? Is the order of aggregates always the same for all the senses?
The same terms are often used at a "microscopic-view" level, at a "day-to-day-view" level and at a "macro-view". This leads to a lot of confusion.
According to the Abhidhamma, feeling / sensation / experience (vedanā) and perception / recognition (saññā) arise simultaneously in every Thought Moment (cittakhaṇa). The Abhidhamma looks at things at a "microscopic-view" level.
The Suttas (MN 18 is an example) describe how sensing leads to thinking. At this "day-to-day-view" level, vedanā (part of the sensing process that is the same for everybody) leads to saññā (start of the thinking process; a subjective process influenced by latent defilements leading to distortion of perception).
The aggregates are a way of describing what constitutes a being (what a being is or what a being does). This is the "macro-view" level that describes the nature of existence. The aggregates do not have a sequence (they are not describing a process), so vedanākkhanda (feeling aggregate) and saññākkhanda (perception aggregate) arise simultaneously.
'Feeling' and 'discrimination' are not only aggregates, they are first and foremost mental factors. As such, they accompany main minds with which they share similarities.
According to Tibetan Lo Rig (Mind and mental factors), the five omnipresent mental factors (intention, attention, contact, feeling, discrimination) are so called because there is not one main mind (such as an instance of an eye-consciousness, ear-consciousness... mental consciousness) that is not associated with the five.
For instance... an eye-consciousness apprehending blue is necessarily accompanied with the five omnipresent mental factors. The main mind and the five share five similarities and are one entity:
1. Time (they arise, abide, cease simultaneously),
2. object of observation,
3. Subjective aspect
Yeshe Gyeltsen's Necklace for Those of Clear Awareness writes:
QUALM: Are a mind and its mental factors one entity or different entities?
RESPONSE: The Treasury of Knowledge (stanza 2.23) says: A mind and its mental factors are definitely simultaneous.
If you want more on this topic such as exposed by Tibetan Geluk scholars, I suggest The Mind and Its Functions, by Geshe Rabten.