Children can respond this way due to many reasons... perhaps:
1) trust/mistrust
2) fear of a parent
3) fear to 'let down' a parent
4) fear of reprisal... and the way someone punishes them
5) fear of consequences
6) fear of a bad temper toward them in light of the incident
7) not feeling 'able' to tell the parent because of the usual way they are handled
8) they know that one parent is more sympathetic than the other
9) they are afraid of the Parent's temper or reaction... because by now the child 'knows' how it goes when they are scolded etc.
10) they know that one Parent is harder to deal with than the other... or one parent is 'stricter' (whether justified or not), than the other...
11) they know that they can go to one parent for comforting more than the other etc.
12) they feel dismissed by a parent no matter what, or not respected, not valued etc.
13) they feel comforted more with one parent than the other
14) they feel more comfortable in expressing themselves with one parent or the other
Sometimes as is typical, a child may run to one parent over the other because they do not want to be scolded or yelled at or what have you.
BUT, since your son went to YOU and opened up to you... it shows he trusts you and can get compassion from you and comforting, rationally. This is good. NEXT, you said your son was "so worried about Daddy being mad at him...." that he didn't go to Daddy, and instead went to you. Again, sounds like 'fear.' He didn't want to even tell Daddy even though he was in pain & Daddy was RIGHT there.
If a child is in ANY kind of pain, they NEED to be able to tell EITHER Parent, and FEEL that they can. What if the pain/injury was serious? Suppose: WHAT IF you were not home when this happened... would your son have just pretended that he was not hurt ALL DAY... and then by the time you came home from work at the end of the day? And that he did this because he was "so worried" about his Dad's reaction. THAT is a LONG LONG time to wait for a child who is hurt... this is not good...For your child.
Now, did you talk with your Hubby about it? You should. To me... a child who is afraid of talking to a parent for a legitimate concern or hurt... is a red light. It has to be remedied... for the CHILD'S sake. The child should come first... when they are hurt/injured physically, or have hurt feelings. At this point, when a child is hurt for any reason... it doesn't matter "who's" fault it was. Their 'hurt' should be addressed first and then they can be talked with about it.
Next, do you KNOW how your Hubby disciplines/handles/corrects/teaches your children when you are not home? Maybe he is more "strict" than you.... but in what way? Does he have a temper problem???
Next, a boy especially, NEEDS to be taught THAT IT IS OKAY TO HAVE FEELINGS AND TO EXPRESS THEM no matter what. Not just be 'strong and silent' and pent up and frustrated or scared to express themselves.
Ideally, YOU as a Mom should know what and how your Hubby disciplines and what 'his' approach is. Obviously...if your son is 'afraid' to tell his Daddy he was hurt/burned.... then that is not good. It's a sign that something has to change... to benefit the well-being of the boys... so that they KNOW that EITHER Parent is a soft place to fall, no matter what and no matter what the situation.
For me, if my Hubby scolds my girl or son too "macho" like.... I tell him... and my Hubby admits it and will tell my children DIRECTLY "I'm sorry... Daddy shouldn't have yelled... I was wrong..." and then he gives them a big hug.... and we ALL talk about it OPENLY. Every parent makes mistakes too, sometimes... and we have to admit that to our child who was 'wronged.' It's important. But, my kids have no 'fear' of their Dad or me. That is the key thing.
If a child has a 'fear' of some adult.... then there must be a reason why. Or, perhaps the parenting 'style' can be adjusted or become more understanding... even a Parent has to 'learn' to be better too... NOT just the child.
Myself growing up, my late Dad, was the one that my sister and I went to, for ANYTHING, good or bad. Why? Because he talked WITH us, did not judge us, did not yell at us for stupid reasons, did not take his anger out on us, respected us, did not dismiss our 'silly' child-like worries, did not flip us off, did not blame us for things wrongly, ALWAYS let us express ourselves and even our deepest insecurities or questions, and ALWAYS ACCEPTED US no matter what. My Mom, was great too, in her own way....but was less accepting and less "warm and fuzzy" than my Dad, and was less understanding. My Dad could be a "mom AND a Dad".... but my Mom was a "Mom." That's hard to explain...but that is the way my Dad was. He was not, in other words, just a 'guy' who was out of touch with his kids or feelings or developmental 'needs.'
So, some kids just gravitate toward one Parent or the other... but as they get older... it gets more so. At least in my/my sister's case. But, then everyone is different. Perhaps your boys just feel more comfortable with you... and they miss you after a long day... and then they just know Mom is always there for them without having to "worry" about how you will react to them.
In any event, it seems to 'bother' you or worry you, that your son reacted this way, in relation to his Dad... thus you posted your question here. You'll get a lot of ideas here.
All the best,
Susan