My kids operate in their 2nd language at school (Gaelic), and they only read/write it until about this point in the year in primary 3, when English begins too - ds is just about to start English at school.
He has already read the first Harry Potter book in English! I was worried about them getting confused between the phonics systems in the different languages (especially the combinations of consonants which are quite complex in Gaelic) but ds has just done it himself, figuring it out and asking if he got stuck. I did some very basic obvious English rules e.g what 'i-n-g' sounded like, but apart from that have left them up to it.
Dd1 is 2 years further on in her English work and is doing well, but she didn't have the urge to read English before it started at school - ds did, so I kind of went with the flow. Dd2 is still in full immersion but was reading the back of the Frosties packet this morning - got a bit stuck with what she was calling "flakkees" (flakes), but making a good attempt.
I suppose where it is different for us is that we are in a deliberately self-selected bilungual setting in the UK, where children have to keep up to the national (Scottish) standards in English, and also we are not cross-cultural, in that the second language has been somewhat imposed on them (we used to live in a very Gaelic speaking area), its not a cultural heritage that either parent has. We are also surrounded by things in English - like cereal packets, road signs etc, which make it a more natural acquisition. Even when we regularly go back to where we used to live, and the children chatter in Gaelic to the next door neighbours and the old lady up the road and stuff, they are still also surrounded by written English every day - I've had to start scanning the front of the newspaper for worrying stories as ds likes to read the headlines!
I do think Mme Lindt is right - mine will read a word using Gaelic phonics, realise it is an English word, and self-correct.
Its fascinating though, watching them learn it. I'm so proud of my bilingual kids (even when they are shouting gaelic abuse at each other over a Wii game!)!