Short answer:
The attack coming from Siege has to be faced before the company decides if they want to enter the site or not. If one or more rivers have been played on the site, the resource player can choose to tap rangers at any moment before, during or after they face the attack from Siege, but in any case that has to be done before they enter the site, and never during the strike sequence.
Explanation:
First, let’s read Siege’s text:
Playable on a Border‐hold or Free‐hold site. A company at this site must face an Orc attack of three strikes at 7 prowess at the beginning of its site phase. At the end of the organization phase, a company at a site with Siege on it must make a roll (or draw a #) and subtract one from the result for every non-Scout character it contains. If this result is less than 5, the company may not move this turn. Discard when the site card is discarded or when the site card is returned to the location deck. Cannot be duplicated on a given site.
We have the rules concerning the site phase:
Site Phase
In the order you decide (i.e., you decide which goes first, second, etc.), each of your companies may:
do nothing or
follow this procedure:
1. Enter its site.
2. If the site has an automatic-attack, it attacks the company. The attack is resolved normally (see Combat).
3. If the site is untapped, a character in the company may attempt to play an item, ally, or faction that is “playable” at that site. Tap the character and the site. Certain resource cards other than items, allies, and factions are playable during the site phase and state the conditions under which they may be played. Such a card only requires an untapped site if it states that the site taps when played.If a tapped site should become untapped, an additional resource may be played that taps the site. Anytime a resource card is played that taps the site, one additional character may tap to play a minor item.
4. Standard Rules Only: One of your characters or your Ringwraith may attempt to influence away one of your opponent’s characters, followers, allies, factions, or items (if it is at the same site). See Influence. ORAgainst Wizard Player Only: One of your companies may make an attack against one of your opponent’s companies (if it is at the same site).
Since Siege’s attack happens at the start of the site phase, and the company has to face this attack no matter what, this committee has found it appropriate to rule that the attack coming from Siege has to be faced before the site phase procedure begins. This means that the company has to face the attack from Siege before they decide whether or not they want to enter the site.
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The interaction between River and Siege has also been brought to our attention (thanks to b_took) After some deliberation, this committee has decided to rule the following:
The CRF entry on River says:
Since the attack from Siege also happens at the beginning of the site phase, there's still time for the resource player to tap a ranger before, during or after they face the attack from Siege (but not during the strike sequence, as per Annotation 18).You have until the beginning of the site phase to tap a ranger, and you may tap the ranger at the beginning of the site phase without entering the site. You must tap one ranger for each river played on the site.