[Vrul]

Try replacing:

local isCaster
local cbCheckFrame = CreateFrame("Frame")
cbCheckFrame:RegisterEvent("PLAYER_LOGIN")
cbCheckFrame:RegisterEvent("PLAYER_SPECIALIZATION_CHANGED")
cbCheckFrame:SetScript("OnEvent", function()
	if playerClass == 'DRUID' then
		isCaster = (GetSpecialization() or 0) % 3 == 1
	elseif playerClass == 'MONK' then
		isCaster = GetSpecialization() == 2
	elseif playerClass == 'PALADIN' then
		isCaster = GetSpecialization() == 1
	elseif playerClass == 'SHAMAN' then
		isCaster = GetSpecialization() ~= 2
	else
		isCaster = playerClass == 'MAGE' or playerClass == 'PRIEST' or playerClass == 'WARLOCK'
	end
 
	print(isCaster)
end)

with:

local detectTalentChange = CreateFrame('Frame')
detectTalentChange:SetScript('OnEvent', function(self)
	if not self.unitFrame then return end

	local isCaster
	if playerClass == 'DRUID' then
		isCaster = (GetSpecialization() or 0) % 3 == 1
	elseif playerClass == 'MONK' then
		isCaster = GetSpecialization() == 2
	elseif playerClass == 'PALADIN' then
		isCaster = GetSpecialization() == 1
	elseif playerClass == 'SHAMAN' then
		isCaster = GetSpecialization() ~= 2
	else
		isCaster = playerClass == 'MAGE' or playerClass == 'PRIEST' or playerClass == 'WARLOCK'
		self:UnregisterAllEvents()
		self:SetScript('OnEvent', nil)
	end

	if isCaster ~= self.isCaster then
		self.isCaster = isCaster
		local Castbar = self.unitFrame.Castbar
		Castbar:ClearAllPoints()
		if isCaster then
			Castbar:SetPoint('TOP', self.unitFrame, 'BOTTOM', 0, -68)
			Castbar:SetStatusBarColor(1, 1, 1)
			Castbar:SetSize(barWidth, 4)
			Castbar:SetBackdrop(backdrop)
			Castbar:SetBackdropColor(0, 0, 0)
			if Castbar.Spark then
				Castbar.Spark:Hide()
			end
		else
			Castbar:SetAllPoints(self.unitFrame.Health)
			Castbar:SetStatusBarColor(1, 1, 1, 0.5)
			Castbar:SetBackdrop(nil)
			if not Castbar.Spark then
				local Spark = Castbar:CreateTexture(nil, 'OVERLAY')
				Spark:SetSize(2, 7)
				Spark:SetTexture(1, 1, 1)
				Castbar.Spark = Spark
			end
			Castbar.Spark:Show()
		end
	end
end)
detectTalentChange:RegisterEvent('ACTIVE_TALENT_GROUP_CHANGED')
detectTalentChange:RegisterEvent('PLAYER_LOGIN')

And change the Castbar portion of your Shared function to:

if(unit=='player' or unit=='target') then
	local Castbar = CreateFrame('StatusBar', nil, self)
	Castbar:SetStatusBarTexture(statusBar)
	Castbar:SetFrameStrata('HIGH')
	self.Castbar = Castbar

	if(unit=='player') then
		detectTalentChange.unitFrame = self
	else
		Castbar:SetPoint('BOTTOM', UIParent, 'CENTER', 0, 200)
		Castbar:SetStatusBarColor(1, 0, 0)
		Castbar:SetBackdrop(backdrop)
		Castbar:SetBackdropColor(0, 0, 0)
		Castbar:SetSize(350, 24)
 
		local Time = Castbar:CreateFontString(nil, 'OVERLAY', 'GameFontNormalSmall')
		Time:SetFont(nameFont, nameFontSize, 'OUTLINE')
		Time:SetTextColor(1, 1, 1)
		Time:SetPoint('RIGHT', Castbar)
		Castbar.Time = Time
 
		local Text = Castbar:CreateFontString(nil, 'OVERLAY', 'GameFontNormalSmall')
		Text:SetFont(nameFont, nameFontSize, 'OUTLINE')
		Text:SetTextColor(1, 1, 1)
		Text:SetPoint('LEFT', Castbar, 'LEFT', 4, 0)
		Castbar.Text = Text
 
		local Icon = Castbar:CreateTexture(nil, 'OVERLAY')
		Icon:SetSize(24, 24)
		Icon:SetPoint('RIGHT', Castbar, 'LEFT', -6, 0)
		Castbar.Icon = Icon
 
		local Shield = Castbar:CreateTexture(nil, 'OVERLAY')
		Shield:SetSize(64, 64)
		Shield:SetPoint('CENTER', Icon, 'CENTER', 12, 0)
		Shield:SetTexture([[Interface\CastingBar\UI-CastingBar-Arena-Shield]])
		Castbar.Shield = Shield
	end
end

The code is untested but is headed in the right direction. It uses the correct event to detect spec changes and can actually change your Castbar when they occur. One issue I'm not sure on is what oUF does with Castbar.Spark behind the scenes and if just hiding/showing it will be sufficient. This code assumes that your unit frames are created before the PLAYER_LOGIN event occurs, if this is not the case then it will need to be adjusted accordingly.